Business Statistics In Practice, 3rd Canadian Edition By Bruce Test Bank

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Business Statistics In Practice, 3rd Canadian Edition By Bruce Test Bank

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WITH ANSWERS
Business Statistics In Practice, 3rd Canadian Edition By Bruce Test Bank

c5

Student: ___________________________________________________________________________

  1. A uniform distribution f(x) is a continuous probability distribution which says the probability that x is in any 2 intervals of equal length is the same.

True    False

 

  1. The mean and median are the same for a normal distribution.

True    False

 

  1. The mean and median are the same for an exponential distribution.

True    False

 

  1. In a statistical study, the random variable X = 1, if the house is colonial, and X = 0 if the house is not colonial, then it is appropriate to model this variable with a continuous probability distribution.

True    False

 

  1. The actual weight of hamburger patties can be modeled using a continuous probability distribution is an example of a continuous random variable.

True    False

 

  1. The number of defective pencils in a lot of 1000 pencils can be modeled using a continuous probability distribution.

True    False

 

  1. For a continuous distribution, P(X 100) = P(X < 100).

True    False

 

  1. All continuous random variables are normally distributed.

True    False

 

  1. For a continuous distribution, the probability that the random variable of interest assumes a one specific value is zero.

True    False

 

  1. The height of a probability curve f(x) at a particular point indicates the value of a probability for a given value of a random variable x.

True    False

 

  1. A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is called a uniform probability distribution.

True    False

 

  1. The exponential probability distribution is used to model a continuous random variable.

True    False

 

  1. The mean of a standard normal distribution is always equal to 1.

True    False

 

  1. The standard deviation of a standard normal distribution is always equal to 1.

True    False

 

  1. The normal probability distribution is a discrete probability distribution.

True    False

 

  1. A continuous random variable may assume only integer values in a given interval.

True    False

 

  1. The z value tells us the number of standard deviations that a value x is from the mean.

True    False

 

  1. If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean.

True    False

 

  1. For a binomial probability experiment, with n = 150 and p = .2, it is appropriate to use the normal approximation to the binomial distribution.

True    False

 

  1. The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?
  2. 500,000
  3. 808,500
  4. 191,500
  5. 308,500
  6. 705,100

 

  1. A standard normal distribution has a mean of _____ and standard deviation of _____.
  2. zero; zero
  3. zero; one
  4. one; one
  5. one; zero
  6. zero; three

 

  1. A property of continuous probability distributions is that:
  2. Like discrete random variables, the probability distribution can be approximated by a smooth curve.
  3. Probabilities for continuous variables can be approximated using discrete random variables.
  4. Unlike discrete random variables, probabilities can be found using tables.
  5. Unlike discrete random variables, the probability that a continuous random variable equals a specific value is zero; that is, P(X = x) = 0.
  6. Unlike discrete random variables, probabilities for continuous random variables can sum to a value greater than 1.

 

  1. The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.
  2. normal
  3. exponential
  4. Poisson
  5. binomial
  6. uniform

 

  1. The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.
  2. less than
  3. greater than
  4. equal to
  5. always equal to
  6. sometimes equal to

 

  1. Let X be a binomial random variable with n = 150 and p = 0.3. Approximate P(X 50).
  2. 0.7881
  3. 0.9909
  4. 0.2119
  5. 0.0091
  6. 0.5644

 

  1. If the random variable X has a mean of and a standard deviation , then    has a mean of ____ and standard deviation of _____.
  2. and
  3. and s
  4. 1 and 0
  5. 0 and 1
  6. Cannot be determined without more information.

 

  1. Which one of the following variables could be modeled using a continuous probability distribution?
  2. The number of students in a university course.
  3. The number of coffees you buy during a school year.
  4. The amount of time you wait in line to buy a coffee.
  5. The number of time somebody sneezes during a 1 hour class.
  6. The number of times somebody shaves during one week.

 

  1. The price-to-earnings ratio for firms in a given industry is distributed according to normal distribution. In this industry, a firm with a standard normal variable value of z = 1:
  2. Has an above average price-to-earning ratio.
  3. Has a below average price-to-earnings ratio.
  4. Has an average price-to-earnings ratio.
  5. Has the minimum possible priError! Hyperlink reference not valid.ce-to-earnings ratio.
  6. Has the maximum possible price-to-earnings ratio.

 

  1. The normal approximation of the binomial distribution is appropriate when:
  2. np 5
  3. nq 5
  4. np 5
  5. nq 5 and np 5
  6. np 5 and nq 5

 

  1. If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour:
  2. Is greater than the proportion earning less than $13 per hour.
  3. Is greater than the proportion earning less than $18 per hour.
  4. Is less than 50%.
  5. Is less than the proportion earning more than the mean wage.
  6. Is less than the proportion earning more than $14 per hour.

 

  1. A students grade on an examination was transformed to a z value which is negative. Therefore, we know that the student scored:
  2. Higher than 16% of the class
  3. Higher than 45% of the class
  4. Above the first quartile
  5. Lower than 16% of the class
  6. Below the mean

 

  1. A study shows that employees that begin their work day at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is:
  2. 0.4
  3. 0.2
  4. 0.1
  5. 0.3
  6. 0.167

 

  1. The relationship between the standard normal random variable z and normal random variable X is that:
  2. Only the normal random variable X is continuous.
  3. Only the standard normal variable z is continuous.
  4. The standard normal variable z counts the number of standard deviations that the value of the normal random variable X is away from its mean.
  5. The values of the standard normal random variable z cannot be negative.
  6. The values of the normal random variable X cannot be negative.

 

The fuel efficiency rating for a mid-size car is normally distributed with a mean of 32 and a standard deviation of 0.8. What is the probability that the rating for a selected mid-size car would be:

 

  1. Less than 33.2?
  2. 4332
  3. 0668
  4. 9332
  5. 8664
  6. 1336

 

  1. More than 33.2?
  2. 4332
  3. 0668
  4. 9332
  5. 8664
  6. 1336

 

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams.

 

  1. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 900 grams?
  2. 4772
  3. 9772
  4. 9544
  5. 0456
  6. 0228

 

  1. If we select one box of cereal at random from this population, what is the probability that it will weigh more than 904 grams?
  2. 8849
  3. 3849
  4. 1151
  5. 7698
  6. 2302

 

  1. We calculated the value of z for a specific box of this brand of cereal and the z value was negative. This negative z value indicates that:
  2. We made a mistake in our calculations, as z must always be a nonnegative number.
  3. The fill weight exceeds 910 grams.
  4. The fill weight is less than 910 grams
  5. The fill weight is equal to 910 grams
  6. The fill weight may be more or less than 910 grams depending on the value of the standard deviation.

 

  1. Which of the following statements is not a property of the normal probability distribution?
  2. The normal distribution is symmetric.
  3. 95.44% of all possible observed values of the random variable x are within three standard deviations of the population mean.
  4. The mean, median, and mode are equal.
  5. The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean.
  6. 68.28% of all possible observed values of the random variable x are within two standard deviations of the population mean.

 

  1. If the random variable of x is normally distributed, ____% of all possible observed values of x will be within three standard deviations of the mean.
  2. 68.26
  3. 95.44
  4. 99.73
  5. 100
  6. Cannot be determined without knowing the actual mean and standard deviation.

 

  1. When a ____________ probability distribution is used to approximate a ________ probability distribution we must make a ____________ correction.
  2. continuous; discrete; continuity
  3. discrete; continuous; continuity
  4. continuous; discrete; finite population
  5. finite population; world; a global
  6. discrete; continuous; finite population

 

  1. A probability distribution that is useful in describing the time or space between successive occurrences of an event is the _______ probability distribution.
  2. uniform
  3. normal
  4. Poisson
  5. exponential
  6. binomial

 

The cashier service time at a local bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time:

 

  1. Exceeds 3 minutes?
  2. 3012
  3. 6988
  4. 4346
  5. 5654
  6. 0821

 

  1. Is no more than 3 minutes?
  2. 3012
  3. 6988
  4. 4346
  5. 5654
  6. 0821

 

  1. Is between 2 and 4 minutes?
  2. 2488
  3. 4493
  4. 2019
  5. 2474
  6. 1170

 

  1. The distance between store outlets in a chain of stores in a large metropolitan city is normally distributed with an average of 50km and a standard deviation of 5km. What is the probability of finding a store no less than 55km away?
  2. 1668
  3. 2443
  4. 1254
  5. 8727
  6. 1587

 

  1. The distance between store outlets in a chain of stores in a large metropolitan city is normally distributed with an average of 50km and a standard deviation of 5km. What is the probability of finding a store between 50km and 60km?
  2. 2747
  3. 3512
  4. 2997
  5. 4772
  6. 5000

 

  1. A normal population has a mean of 10 and a variance of 4. What is P(X < 6)?
  2. 0228
  3. 4772
  4. 0398
  5. 0438
  6. 4948

 

  1. A normal population has a mean of 10 and a variance of 4. What is P(X > 7)?
  2. 6844
  3. 9987
  4. 8913
  5. 7750
  6. 9332

 

  1. The weight of a product is normally distributed with a standard deviation of 0.5 grams. If the production manager wants no more than 5% of the products to weigh more than 5.1 grams, then the average weight should be _____.
  2. 4.278
  3. 4.833
  4. 4.900
  5. 5.212
  6. 5.100

 

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20.

 

  1. What percentage of the time will the number of boxes received weekly be greater than 200?
  2. 6844
  3. 5000
  4. 8913
  5. 7500
  6. 6332

 

  1. What percentage of the time will the number of boxes received weekly be less than 160?
  2. 0844
  3. 0987
  4. 0913
  5. 0750
  6. 0228

 

  1. What percentage of the time will the number of boxes received weekly be between 180 and 210?
  2. 5328
  3. 5987
  4. 4913
  5. 7750
  6. 5332

 

  1. What percentage of the time will the number of boxes received weekly be greater than 210 or less than 180?
  2. 5328
  3. 5987
  4. 4913
  5. 4672
  6. 5332

 

  1. A movie theatre manager knows that the number of patrons per movie is normally distributed with a mean of 200 and a standard deviation of 20. What is the number of patrons, x, where 50% are less than x?
  2. 532
  3. 597
  4. 413
  5. 200
  6. 332

 

  1. A movie theatre manager knows that the number of patrons per movie is normally distributed with a mean of 200 and a standard deviation of 20. What is the number of patrons, x, where 80% are less than x?
  2. 216.8
  3. 597.2
  4. 413.3
  5. 297.2
  6. 332.8

 

A company must decide their contribution to their pension plan based on the probability distribution of the length of life of their retired employees. Suppose the probability distribution of the lifetimes of their employees is approximately a normal distribution with = 74 years and = 8.6 years.

 

  1. What percentage of their retired employees would receive payments beyond age 76?
  2. 53.28%
  3. 59.87%
  4. 49.13%
  5. 46.72%
  6. 40.90%

 

  1. What percentage of their retired employees would receive payments beyond age 85?
  2. 13.28%
  3. 19.87%
  4. 19.13%
  5. 10.03%
  6. 10.90%

 

  1. Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25. Using this information, what percentage of the population scores greater than 15?
  2. 53.28%
  3. 59.87%
  4. 49.13%
  5. 50.00%
  6. 40.00%

 

  1. Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25. Using this information, what percentage of the population scores between 10 and 20?
  2. 53.28%
  3. 59.87%
  4. 49.13%
  5. 50.00%
  6. 68.26%

 

  1. The z-value tells us the number of _____ that a value of x is from the mean.

________________________________________

 

  1. A probability distribution that describes the time or space between successive occurrences of an event is a(n) _____ probability distribution.

________________________________________

 

  1. A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is a(n) _____ distribution.

________________________________________

 

  1. The specific shape of each normal distribution is determined by its _____ and _____.

________________________________________

 

  1. The number of standard deviations that a value x is from the mean is a _____.

________________________________________

 

  1. The area under the curve of a valid continuous probability distribution must equal _____.

________________________________________

 

  1. Given that X is a normal random variable, the probability that a given value of X is below its mean is ________________.

________________________________________

 

  1. A normal distribution with mean zero and a standard deviation one is called the _____ normal distribution.

________________________________________

 

  1. The thickness of randomly selected metal piece is a ___________ random variable.

________________________________________

 

  1. __________ values of the standard deviation results in a normal curve that is wider and flatter.

________________________________________

 

  1. _____________ values of the standard deviation results in a normal curve that is narrower and more peaked.

________________________________________

 

  1. The mean of a standard normal distribution is always equal to _______.

________________________________________

 

  1. The standard deviation of a standard normal distribution is always equal to _____.

________________________________________

 

  1. For a normal population with a mean of 10 and a variance 4, the P(X 10) is ___.

________________________________________

 

  1. If the random variable of x is normally distributed, ____ % of all possible observed values of x will be within two standard deviations of the mean.

________________________________________

 

  1. The time of travel from a persons apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes. If they leave home at 9:05 AM, what is the probability that they will get to the station between 9:25 and 9:30 AM?

 

 

 

 

 

 

 

The average distance between store outlets in a chain of stores in a large metropolitan city is 50km and has a standard deviation of 5km. What is the probability of finding a store:

 

  1. No less than 55km away?

 

 

 

 

 

 

 

  1. Between 50 km and 60 km?

 

 

 

 

 

 

 

  1. If the scores on an aptitude test are normally distributed with mean 500 and standard deviation 100, what proportion of the test scores are less than 585?

 

 

 

 

 

 

 

  1. If x is a binomial random variable where n = 100 and p = .1, find the probability that x is less than or equal to 10 using the normal approximation to the binomial.

 

 

 

 

 

 

 

  1. What is the probability that a random variable having a standard normal distribution is between .87 and 1.28?

 

 

 

 

 

 

 

  1. The probability that an appliance is in repair is .5. If an apartment complex has 100 such appliances, what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial.

 

 

 

 

 

 

 

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly:

 

  1. Less than 4.66 hours?

 

 

 

 

 

 

 

  1. More than 4.80 hours?

 

 

 

 

 

 

 

  1. Between 4.70 and 4.82 hours?

 

 

 

 

 

 

 

  1. What is the probability that a standard normal random variable will be between -2 and 2?

 

 

 

 

 

 

 

  1. What is the probability that a standard normal random variable will be between .3 and 3.2?

 

 

 

 

 

 

 

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last:

 

  1. More than 1,200 hours?

 

 

 

 

 

 

 

  1. Less than 800 hours?

 

 

 

 

 

 

 

The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime:

 

  1. Exceeds 1,000 days?

 

 

 

 

 

 

 

  1. Is greater than or equal to 700 days?

 

 

 

 

 

 

 

  1. The time between breakdowns of an alarm system is exponentially distributed with mean 10 days. What is the probability that there are no breakdowns on a given day?

 

 

 

 

 

 

 

An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed.

 

  1. What proportion of tests has scores over 90?

 

 

 

 

 

 

 

  1. What raw score corresponds to the 70th percentile?

 

 

 

 

 

 

 

  1. Suppose the daily change in price of a stock is normally distributed with mean = .20 and standard deviation = .30. What price change is associated with the 25th percentile?

 

 

 

 

 

 

 

  1. If a personnel aptitude test score of 32 has a z-score of 1.2, and a score of 24 has a z-score of -.4, what is the mean test score of the distribution?

 

 

 

 

 

 

 

Consider a normal population with a mean of 10 and a standard deviation 2.

 

  1. Find P(X > 13).

 

 

 

 

 

 

 

  1. Find P(X < 12).

 

 

 

 

 

 

 

  1. Find P(X = 10).

 

 

 

 

 

 

 

Consider a normal population with a mean of 10 and a variance of 4.

 

  1. Find P(X < 6).

 

 

 

 

 

 

 

  1. Find P(X > 7).

 

 

 

 

 

 

 

  1. Find P(X > 18).

 

 

 

 

 

 

 

  1. Find P(X 10).

 

 

 

 

 

 

 

The temperature for the month of July with the humidex factor is normally distributed with a mean of 30.05C with a standard deviation of 0.2C.

 

  1. What is the probability that a daily July temperature taken at random will be less than 29.75C?

 

 

 

 

 

 

 

  1. What is the probability that a daily July temperature taken at random from the population is between 30.25C and 30.65C?

 

 

 

 

 

 

 

  1. What is the probability that a daily July temperature taken at random will be less than 29.75C?

 

 

 

 

 

 

 

  1. What is the probability that a daily July temperature taken at random from the population is between 29.75C and 30.5C?

 

 

 

 

 

 

 

  1. If x is a binomial random variable where n = 100 and p = .2, find the probability that x is less than or equal to 18 using the normal approximation to the binomial.

 

 

 

 

 

 

 

The weight of a product is normally distributed with a mean of four grams and a variance of .25 squared grams. What is the probability that a randomly selected unit from a recently manufactured batch weighs:

 

  1. More than 5 grams?

 

 

 

 

 

 

 

  1. No more than 3.5 grams?

 

 

 

 

 

 

 

  1. More than 3.75 grams?

 

 

 

 

 

 

 

  1. The weight of a product is normally distributed with a standard deviation of .5 grams. What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 5.1 grams?

 

 

 

 

 

 

 

  1. The weight of a product is normally distributed with a standard deviation of .5 grams. What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 4.8 grams?

 

 

 

 

 

 

 

  1. The weight of a product is normally distributed with a mean 5 grams. A randomly selected unit of this product weighs 7.1 grams. The probability of a unit weighing more than 7.1 grams is .0014. The production supervisor has lost files containing various pieces of information regarding this process including the standard deviation. Determine the value of standard deviation for this process.

 

 

 

 

 

 

 

The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed.

 

  1. What is the probability a subscriber will spend at least 1 hour reading the paper?

 

 

 

 

 

 

 

  1. What is the probability a subscriber will spend no more than 30 minutes reading the paper?

 

 

 

 

 

 

 

  1. For the 10% who spend the most time reading the paper, how much time do they spend?

 

 

 

 

 

 

 

At a Great Lakes nuclear power plant, lake water is used as part of the cooling system. This raises the temperature of the water that is discharged back into the lake. The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25 C.

 

  1. What is the probability that the temperature increase will be less than 20 C?

 

 

 

 

 

 

 

  1. What is the probability that the temperature increase will be between 20 and 22 C?

 

 

 

 

 

 

 

  1. Suppose that a temperature increase of more than 18 C is considered to be potentially dangerous to the environment. What is the probability that at any point of time, the temperature increase is potentially dangerous?

 

 

 

 

 

 

 

  1. What is the expected value of the temperature increase?

 

 

 

 

 

 

 

  1. What is the standard deviation of the temperature increase?

 

 

 

 

 

 

 

During the past six months, 73.2% of households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.

 

  1. Find the probability that a household spent less than $5.00

 

 

 

 

 

 

 

  1. Find the probability that a household spent more than $10.00

 

 

 

 

 

 

 

  1. Find the probability that a household spent more than $16.00

 

 

 

 

 

 

 

  1. What proportion of the households spent between $5.00 and $9.00?

 

 

 

 

 

 

 

  1. 99% of the households spent less than what amount?

 

 

 

 

 

 

 

  1. 80% of the households spent more than what amount?

 

 

 

 

 

 

 

Suppose that the times required for a cable company to fix cable problems in its customers homes are uniformly distributed between 40 minutes and 65 minutes.

 

  1. What is the probability that a randomly selected cable repair visit will take at least 50 minutes?

 

 

 

 

 

 

 

  1. What is the probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean?

 

 

 

 

 

 

 

Suppose that the waiting time for a pizza to be delivered to an individuals residence has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time:

 

  1. Between 15 and 45 minutes

 

 

 

 

 

 

 

  1. At least 10 minutes

 

 

 

 

 

 

 

  1. No more than 22 minutes

 

 

 

 

 

 

 

  1. Suppose that in an effort to provide better service to the public, the manager of the pizza delivery service is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15% of the customers should receive this discount. What are the number of minutes they need to wait to receive the discount?

 

 

 

 

 

 

 

  1. Complete the following statement: Only 20% of the individuals wait less than _____ minutes.

 

 

 

 

 

 

 

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9.

 

  1. What is the probability of getting a grade of 91 or less on this exam?

 

 

 

 

 

 

 

  1. What percentage of students scored between 65 and 89?

 

 

 

 

 

 

 

  1. What percentage of students scored between 81 and 89?

 

 

 

 

 

 

 

  1. Only 5% of the students taking the test scored higher than what grade?

 

 

 

 

 

 

 

  1. A manufacturer of personal computers sets tests competing brands and finds that the amounts of energy they require are normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh.

If the lowest 25% and the highest 30% are not included in a second round of tests, what are the upper and lower limits for the energy amounts of the remaining sets?

 

 

 

 

 

 

 

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.

 

  1. What is the probability that a randomly selected depth is less than 3.60 m?

 

 

 

 

 

 

 

  1. What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?

 

 

 

 

 

 

 

  1. What is the expected value of the water depth?

 

 

 

 

 

 

 

  1. What is the standard deviation of the water depth?

 

 

 

 

 

 

 

  1. What is the probability that a randomly selected depth is within 1 standard deviation of the mean?

 

 

 

 

 

 

 

The price of an energy sports drink is normally distributed with an average of $2.25 and a standard deviation of $0.15 across store outlets.

 

  1. What is the probability that a randomly selected drink will cost between $2.00 and $3.00?

 

 

 

 

 

 

 

  1. What is the probability that a randomly selected drink will cost between $2.00 and $2.50?

 

 

 

 

 

 

 

  1. What is the probability that a randomly selected drink will cost more than $2.50?

 

 

 

 

 

 

 

  1. What price will 77% of the drink prices fall above?

 

 

 

 

 

 

 

  1. Between what two values (in dollars) symmetrically distributed around the population mean will 80% of the drink prices fall?

 

 

 

 

 

 

 

  1. Find z when the area between 0 and z is .4750

 

 

 

 

 

 

 

  1. Find z when the area to the right of z is .1314

 

 

 

 

 

 

 

  1. Find z when the area to the left of z is .6700

 

 

 

 

 

 

 

  1. Find z when the area between z and -z is .9030

 

 

 

 

 

 

 

  1. Find z when the area to the left of z is .05

 

 

 

 

 

 

 

A paint sprayer coats a metal surface with a layer of paint between 0.43 and 1.23 millimeters thick. The thickness of the coat of paint is approximately uniformly distributed.

 

  1. What are the mean and standard deviation of the thickness of the coat of paint on the metal surface?

 

 

 

 

 

 

 

  1. What is the probability that paint from this sprayer on any given metal surface will be between 0.75 and 1.05 millimeters thick?

 

 

 

 

 

 

 

  1. The yearly number of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of 105 and a standard deviation of 35. What is the yearly number at which 35% of the employees fall at or below?

 

 

 

 

 

 

 

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received weekly be

 

  1. Greater than 200

 

 

 

 

 

 

 

  1. Less than 160

 

 

 

 

 

 

 

  1. Between 180 and 210

 

 

 

 

 

 

 

  1. Greater than 210 or Less than 180

 

 

 

 

 

 

 

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. Determine the number of boxes, x, where

 

  1. 50% of the number of boxes received weekly are less than x

 

 

 

 

 

 

 

  1. 80% of the number of boxes received weekly are less than x

 

 

 

 

 

 

 

A company must decide their contribution to their pension plan based on the probability distribution of the length of life of their retired employees. Suppose the probability distribution of the lifetimes of their employees is approximately a normal distribution with = 74 years and = 8.6 years. What percentage of their retired employees would receive payments:

 

  1. Beyond age 76

 

 

 

 

 

 

 

  1. Beyond age 85

 

 

 

 

 

 

 

  1. Complete the following statement: Only 12.5% of their retired employees will receive payment beyond age ______.

 

 

 

 

 

 

 

Suppose the distribution of personality test scores is normally distributed with a mean of 15 and a variance of 25.

 

  1. What percentage of the population scores greater than 15?

 

 

 

 

 

 

 

  1. What percentage of the population scores between 10 and 20?

 

 

 

 

 

 

 

  1. What is the probability of finding a person who scores less than 10?

 

 

 

 

 

 

 

  1. If X is an exponential random variable, then the probability X falls below its mean value is _____.

 

 

 

 

 

 

 

 

 

c5 Key

 

  1. A uniform distribution f(x) is a continuous probability distribution which says the probability that x is in any 2 intervals of equal length is the same.

TRUE

 

 

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Bowerman Chapter 05 #1

Difficulty: Medium

Learning Objective: 05-02 Compute probabilities using the uniform distribution

 

  1. The mean and median are the same for a normal distribution.

TRUE

 

 

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Bowerman Chapter 05 #2

Difficulty: Easy

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. The mean and median are the same for an exponential distribution.

FALSE

 

 

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Bowerman Chapter 05 #3

Difficulty: Easy

Learning Objective: 05-07 Compute probabilities using the exponential distribution

 

  1. In a statistical study, the random variable X = 1, if the house is colonial, and X = 0 if the house is not colonial, then it is appropriate to model this variable with a continuous probability distribution.

FALSE

 

 

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Bowerman Chapter 05 #4

Difficulty: Easy

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. The actual weight of hamburger patties can be modeled using a continuous probability distribution is an example of a continuous random variable.

TRUE

 

 

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Bowerman Chapter 05 #5

Difficulty: Medium

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. The number of defective pencils in a lot of 1000 pencils can be modeled using a continuous probability distribution.

FALSE

 

 

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Bowerman Chapter 05 #6

Difficulty: Medium

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. For a continuous distribution, P(X 100) = P(X < 100).

TRUE

 

 

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Bowerman Chapter 05 #7

Difficulty: Medium

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. All continuous random variables are normally distributed.

FALSE

 

 

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Bowerman Chapter 05 #8

Difficulty: Medium

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. For a continuous distribution, the probability that the random variable of interest assumes a one specific value is zero.

TRUE

 

 

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Bowerman Chapter 05 #9

Difficulty: Medium

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. The height of a probability curve f(x) at a particular point indicates the value of a probability for a given value of a random variable x.

FALSE

 

 

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Bowerman Chapter 05 #10

Difficulty: Easy

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is called a uniform probability distribution.

TRUE

 

 

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Bowerman Chapter 05 #11

Difficulty: Medium

Learning Objective: 05-02 Compute probabilities using the uniform distribution

 

  1. The exponential probability distribution is used to model a continuous random variable.

TRUE

 

 

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Bowerman Chapter 05 #12

Difficulty: Easy

Learning Objective: 05-07 Compute probabilities using the exponential distribution

 

  1. The mean of a standard normal distribution is always equal to 1.

FALSE

 

 

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Bowerman Chapter 05 #13

Difficulty: Easy

Learning Objective: N/A

 

  1. The standard deviation of a standard normal distribution is always equal to 1.

TRUE

 

 

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Bowerman Chapter 05 #14

Difficulty: Easy

Learning Objective: N/A

 

  1. The normal probability distribution is a discrete probability distribution.

FALSE

 

 

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Bowerman Chapter 05 #15

Difficulty: Easy

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. A continuous random variable may assume only integer values in a given interval.

FALSE

 

 

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Bowerman Chapter 05 #16

Difficulty: Easy

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. The z value tells us the number of standard deviations that a value x is from the mean.

TRUE

 

 

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Bowerman Chapter 05 #17

Difficulty: Easy

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean.

FALSE

 

 

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Bowerman Chapter 05 #18

Difficulty: Easy

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. For a binomial probability experiment, with n = 150 and p = .2, it is appropriate to use the normal approximation to the binomial distribution.

TRUE

 

 

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Bowerman Chapter 05 #19

Difficulty: Medium

Learning Objective: 05-06 Approximate binomial probabilities using the normal distribution

 

  1. The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?
  2. 500,000
  3. 808,500
  4. 191,500
  5. 308,500
  6. 705,100

 

 

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Bowerman Chapter 05 #20

Difficulty: Hard

Learning Objective: 05-04 Compute probabilities using the normal distribution

 

  1. A standard normal distribution has a mean of _____ and standard deviation of _____.
  2. zero; zero
  3. zero; one
  4. one; one
  5. one; zero
  6. zero; three

 

 

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Bowerman Chapter 05 #21

Difficulty: Easy

Learning Objective: N/A

 

  1. A property of continuous probability distributions is that:
  2. Like discrete random variables, the probability distribution can be approximated by a smooth curve.
  3. Probabilities for continuous variables can be approximated using discrete random variables.
  4. Unlike discrete random variables, probabilities can be found using tables.
  5. Unlike discrete random variables, the probability that a continuous random variable equals a specific value is zero; that is, P(X = x) = 0.
  6. Unlike discrete random variables, probabilities for continuous random variables can sum to a value greater than 1.

 

 

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Bowerman Chapter 05 #22

Difficulty: Hard

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.
  2. normal
  3. exponential
  4. Poisson
  5. binomial
  6. uniform

 

 

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Bowerman Chapter 05 #23

Difficulty: Medium

Learning Objective: 05-07 Compute probabilities using the exponential distribution

 

  1. The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.
  2. less than
  3. greater than
  4. equal to
  5. always equal to
  6. sometimes equal to

 

 

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Bowerman Chapter 05 #24

Difficulty: Medium

Learning Objective: N/A

 

  1. Let X be a binomial random variable with n = 150 and p = 0.3. Approximate P(X 50).
  2. 0.7881
  3. 0.9909
  4. 0.2119
  5. 0.0091
  6. 0.5644

 

 

Bowerman Chapter 05 #25

Difficulty: Medium

Learning Objective: 05-06 Approximate binomial probabilities using the normal distribution

 

  1. If the random variable X has a mean of and a standard deviation , then    has a mean of ____ and standard deviation of _____.
  2. and
  3. and s
  4. 1 and 0
  5. 0 and 1
  6. Cannot be determined without more information.

 

 

Bowerman Chapter 05 #26

Difficulty: Medium

Learning Objective: N/A

 

  1. Which one of the following variables could be modeled using a continuous probability distribution?
  2. The number of students in a university course.
  3. The number of coffees you buy during a school year.
  4. The amount of time you wait in line to buy a coffee.
  5. The number of time somebody sneezes during a 1 hour class.
  6. The number of times somebody shaves during one week.

 

 

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Bowerman Chapter 05 #27

Difficulty: Easy

Learning Objective: 05-01 Explain the purpose of a continuous probability distribution

 

  1. The price-to-earnings ratio for firms in a given industry is distributed according to normal distribution. In this industry, a firm with a standard normal variable value of z = 1:
  2. Has an above average price-to-earning ratio.
  3. Has a below average price-to-earnings ratio.
  4. Has an average price-to-earnings ratio.
  5. Has the minimum possible priError! Hyperlink reference not valid.ce-to-earnings ratio.
  6. Has the maximum possible price-to-earnings ratio.

 

 

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Bowerman Chapter 05 #28

Difficulty: Medium

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. The normal approximation of the binomial distribution is appropriate when:
  2. np 5
  3. nq 5
  4. np 5
  5. nq 5 and np 5
  6. np 5 and nq 5

 

 

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Bowerman Chapter 05 #29

Difficulty: Medium

Learning Objective: 05-06 Approximate binomial probabilities using the normal distribution

 

  1. If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour:
  2. Is greater than the proportion earning less than $13 per hour.
  3. Is greater than the proportion earning less than $18 per hour.
  4. Is less than 50%.
  5. Is less than the proportion earning more than the mean wage.
  6. Is less than the proportion earning more than $14 per hour.

 

 

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Bowerman Chapter 05 #30

Difficulty: Hard

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. A students grade on an examination was transformed to a z value which is negative. Therefore, we know that the student scored:
  2. Higher than 16% of the class
  3. Higher than 45% of the class
  4. Above the first quartile
  5. Lower than 16% of the class
  6. Below the mean

 

 

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Bowerman Chapter 05 #31

Difficulty: Medium

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. A study shows that employees that begin their work day at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is:
  2. 0.4
  3. 0.2
  4. 0.1
  5. 0.3
  6. 0.167

 

 

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Bowerman Chapter 05 #32

Difficulty: Medium

Learning Objective: 05-02 Compute probabilities using the uniform distribution

 

  1. The relationship between the standard normal random variable z and normal random variable X is that:
  2. Only the normal random variable X is continuous.
  3. Only the standard normal variable z is continuous.
  4. The standard normal variable z counts the number of standard deviations that the value of the normal random variable X is away from its mean.
  5. The values of the standard normal random variable z cannot be negative.
  6. The values of the normal random variable X cannot be negative.

 

 

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Bowerman Chapter 05 #33

Difficulty: Hard

Learning Objective: 05-03 Describe the properties of the normal distribution

 

The fuel efficiency rating for a mid-size car is normally distributed with a mean of 32 and a standard deviation of 0.8. What is the probability that the rating for a selected mid-size car would be:

 

 

Bowerman Chapter 05

 

  1. Less than 33.2?
  2. 4332
  3. 0668
  4. 9332
  5. 8664
  6. 1336

 

 

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Bowerman Chapter 05 #34

Difficulty: Medium

Learning Objective: 05-04 Compute probabilities using the normal distribution

 

  1. More than 33.2?
  2. 4332
  3. 0668
  4. 9332
  5. 8664
  6. 1336

 

 

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Bowerman Chapter 05 #35

Difficulty: Medium

Learning Objective: 05-04 Compute probabilities using the normal distribution

 

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams.

 

 

Bowerman Chapter 05

 

  1. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 900 grams?
  2. 4772
  3. 9772
  4. 9544
  5. 0456
  6. 0228

 

 

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Bowerman Chapter 05 #36

Difficulty: Medium

Learning Objective: 05-04 Compute probabilities using the normal distribution

 

  1. If we select one box of cereal at random from this population, what is the probability that it will weigh more than 904 grams?
  2. 8849
  3. 3849
  4. 1151
  5. 7698
  6. 2302

 

 

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Bowerman Chapter 05 #37

Difficulty: Medium

Learning Objective: 05-04 Compute probabilities using the normal distribution

 

  1. We calculated the value of z for a specific box of this brand of cereal and the z value was negative. This negative z value indicates that:
  2. We made a mistake in our calculations, as z must always be a nonnegative number.
  3. The fill weight exceeds 910 grams.
  4. The fill weight is less than 910 grams
  5. The fill weight is equal to 910 grams
  6. The fill weight may be more or less than 910 grams depending on the value of the standard deviation.

 

 

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Bowerman Chapter 05 #38

Difficulty: Easy

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. Which of the following statements is not a property of the normal probability distribution?
  2. The normal distribution is symmetric.
  3. 95.44% of all possible observed values of the random variable x are within three standard deviations of the population mean.
  4. The mean, median, and mode are equal.
  5. The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean.
  6. 68.28% of all possible observed values of the random variable x are within two standard deviations of the population mean.

 

 

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Bowerman Chapter 05 #39

Difficulty: Medium

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. If the random variable of x is normally distributed, ____% of all possible observed values of x will be within three standard deviations of the mean.
  2. 68.26
  3. 95.44
  4. 99.73
  5. 100
  6. Cannot be determined without knowing the actual mean and standard deviation.

 

 

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Bowerman Chapter 05 #40

Difficulty: Easy

Learning Objective: 05-03 Describe the properties of the normal distribution

 

  1. When a ____________ probability distribution is used to approximate a ________ probability distribution we must make a ____________ correction.
  2. continuous; discrete; continuity
  3. discrete; continuous; continuity
  4. continuous; discrete; finite population
  5. finite population; world; a global
  6. discrete; continuous; finite population

 

 

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Bowerman Chapter 05 #41

Difficulty: Medium

Learning Objective: 05-06 Approximate binomial probabilities using the normal distribution

 

  1. A probability distribution that is useful in describing the time

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