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Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions

A discrete random variable can have the values x = 3, x = 8, or x = 10, and the respective probabilities are 0.2, 0.7, and 0.1. Determine the mean, variance, and standard deviation of x.
What is the difference between a continuous probability distribution and a discrete probability distribution?
The Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year was $1.55. If we assume a normal distribution and a standard deviation of σ = $0.20, what proportion of passenger trips produced a revenue of a. less than $1.55? b. between $1.15 and
In 2007, the average conventional first mortgage for new single-family homes was $360,000. Assuming a normal distribution and a standard deviation of σ = $30,000, what proportion of the mortgages were Source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 726. a. more
In 2009, the average charge for tax preparation by H&R Block, Inc. was $187. Assuming a normal distribution and a standard deviation of σ = $20, what proportion of H&R Block’s tax preparation fees were a. more than $187? b. between $147 and $227? c. between $167 and $207? d. more than $227?
It has been reported that the average hotel check-in time, from curbside to delivery of bags into the room, is 12.0 minutes. An Li has just left the cab that brought her to her hotel. Assuming a normal distribution with a standard deviation of 2.0 minutes, what is the probability that the time
The average American family of four spends $5000 per year on food prepared at home. Assuming a normal distribution with a standard deviation of $1000 and a randomly selected American family of four, what is the probability that the family’s annual spending for food prepared at home will be: a.
On average, commuters in the Los Angeles, California, area require 30.0 minutes to get to work. Assume a normal distribution with a standard deviation of 5.0 minutes and a randomly selected Los Angeles-area commuter named Jamal. a. What is the probability that Jamal will require more than 45.0
In the standard normal distribution, approximately what values of z correspond to the a. First and third quartiles? b. First and ninth deciles? c. 23rd and 77th percentiles?
A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score: a. x = $1000 b. x = $750 c. x = $1100 d. x = $950 e. x = $1225
A continuous random variable, x, is normally distributed with a mean of 200 grams and a standard deviation of 25 grams. Convert each of the following x values into its corresponding z-score: a. x = 150 b. x = 180 c. x = 200 d. x = 285 e. x = 315
What is a probability density function and how is it relevant to the determination of probabilities associated with a continuous random variable?
Using the standard normal table, find the following probabilities associated with z: a. P(0.00 ≤ z ≤ 1.25) b. P(21.25 ≤ z ≤ 0.00) c. P(21.25 ≤ z ≤ 1.25)
Using the standard normal table, find the following probabilities associated with z: a. P(0.00 ≤ z ≤ 1.10) b. P(z ≥ 1.10) c. P(z ≤ 1.35)
Using the standard normal table, find the following probabilities associated with z: a. P(- 0.36 ≤ z ≤ 0.00) b. P(z ≤ - 0.36) c. P(z ≥ 20.43)
Using the standard normal table, find the following probabilities associated with z: a. P(-1.96 ≤ z ≤ 1.27) b. P(0.29 ≤ z ≤ 1.00) c. P(-2.87 ≤ z ≤ -1.22)
Using the standard normal table, determine a z value (to two decimal places) such that the a. Cumulative area to z is 0.7486. b. Cumulative area to z is 0.0735. c. Area between z and positive infinity is 0.3508. d. Area between z and positive infinity is 0.0212.
Using the standard normal table, determine a z value (to two decimal places) such that the a. Cumulative area to z is 0.70. b. Cumulative area to z is 0.10. c. Area between z and negative infinity is 0.54. d. Area between z and positive infinity is 0.30.
For the normal distribution described in Exercise 7.10, what is the probability that a randomly selected passenger trip would have produced a revenue a. Between $1.55 and $1.80? b. Over $1.90? c. Under $1.25?
For the normal distribution described in Exercise 7.11, what is the probability that a randomly selected first mortgage would have been for an amount a. Between $305,000 and $325,000? b. Over $325,000? c. Under $390,000?
For the normal distribution described in Exercise 7.12, what is the probability that a randomly selected tax preparation customer would have paid a fee a. Between $150 and $180? b. Under $140? c. Over $220?
For the normal distribution described in Exercise 7.15, what is the probability that Jamal’s commuting time to work today will be a. Less than 29 minutes? b. Between 29 and 33 minutes? c. More than 32 minutes?
Why is the total area beneath a probability density function equal to 1.0?
For the normal distribution described in Exercise 7.15, what commuting time will be exceeded on only 10% of Jamal’s commuting days? In exercise Assume a normal distribution with a standard deviation of 5.0 minutes and a randomly selected Los Angeles-area commuter named Jamal.
For the normal distribution described in Exercise 7.11, what first-mortgage amount would have been exceeded by only 5% of the mortgage customers? In exercise Assuming a normal distribution and a standard deviation of σ = $30,000, what proportion of the mortgages were Source: Bureau of the Census,
For the normal distribution described in Exercise 7.12, what tax preparation fee would have been exceeded by 90% of the tax preparation customers?In exerciseAssuming a normal distribution and a standard deviation of σ = $20, what proportion of H&R Block’s tax preparation fees were
It has been reported that households in the West spend an annual average of $6050 for groceries. Assume a normal distribution with a standard deviation of $1500. Source: David Stuckey and Sam Ward, “Home Cooked,” USA Today, July 25, 2006, p. 1A. a. What is the probability that a randomly
Andre is a fearless circus performer who gets shot from a special cannon during the grand finale of the show and is supposed to land on a safety net at the other side of the arena. The distance he travels varies, but is normally distributed with a mean of 150 feet and a standard deviation of 10
Drying times for newly painted microwave oven cabinets are normally distributed with a mean of2.5 minutes and a standard deviation of 0.25 minutes. After painting, each cabinet is mated with its electronic modules and mechanical components. The production manager must decide how much time to allow
KleerCo supplies an under-hood, emissions control air pump to the automotive industry. The pump is vacuum powered and works while the engine is operating, cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle in which it is installed has covered
The KleerCo company in Exercise 7.36 would like to design a more durable pump so that no more than 2% of original-equipment pumps are returned under free warranty, and the standard deviation continues to be 10,000 miles. What will the new average service life have to be in order for the new pump
A battery manufacturer has just begun distribution of its SuperVolt, a 6-volt lantern battery for outdoor enthusiasts. Prototype tests of the new battery found the average lifetime in continuous use to be 8 hours, with a standard deviation of 2 hours. Battery lifetimes in such applications have
What is the correction for continuity and why is it employed when the normal distribution is used in approximating the binomial distribution?
In a certain binomial distribution, π = 0.25 and n = 40. In using the normal approximation,a. What are the mean and standard deviation of the corresponding normal distribution?b. If x = the number of “successes” among the 40 observations, determine the following: P(x = 8), P(12 ≤ x ≤ 16),
In a certain binomial distribution, π = 0.30 and n = 20. In using the normal approximation,a. What are the mean and standard deviation of the corresponding normal distribution?b. If x = the number of “successes” among the 20 observations, determine the following: P(x = 5), P(4 ≤ x ≤ 7),
Approximately 80% of American families have some form of life insurance coverage. For a randomly selected sample of n = 15 families, and the discrete random variable x = the number of families in the sample who are covered by life insurance:a. Calculate the mean and the standard deviation of the
About 40% of new single-family homes completed in the United States during 2007 were heated with electricity. For a randomly selected sample of 20 new singlefamily homes completed during that year and the discrete random variable, x = the number of homes in this group heated with electricity:a.
Of all individual tax returns filed in the United States during the 2009 tax filing season, 15.8% were prepared by H&R Block. For a randomly selected sample of 900 tax returns filed during this period, use the normal approximation to the binomial distribution in determining the probability that
The Electronic Industries Association reports that about 50% of U.S. households have a camcorder. For a randomly selected sample of 800 U.S. households, use the normal approximation to the binomial distribution in determining the probability that at least 410 of these households have a camcorder.
Repeat Exercise 7.45, but without using the correction for continuity (i.e., the discrete random variable, x, is not replaced by the interval x – 0.5 to x + 0.5). Does your answer differ appreciably from that obtained in Exercise 7.45? If not, comment on the need for using the correction for
Repeat Exercise 7.46, but without using the correction for continuity (i.e., the discrete random variable, x, is not replaced by the interval x – 0.5 to x + 0.5). Does your answer differ appreciably from that obtained in Exercise 7.46? If not, comment on the need for using the correction for
What is the relationship between the Poisson distribution and the exponential distribution?
A random variable is Poisson distributed with λ = 1.5 occurrences per hour. For the corresponding exponential distribution, and x = hours until the next occurrence, identify the mean of x and determine the following: a. P(x ≥ 0.5) b. P(x ≥ 1.0) c. P(x ≥ 1.5) d. P(x ≥ 2.0)
A random variable is Poisson distributed with λ = 0.02 occurrences per minute. For the corresponding exponential distribution, and x = minutes until the next occurrence, identify the mean of x and determine the following: a. P(x ≥ 30.0) b. P(x ≥ 40.0) c. P(x ≥ 50.0) d. P(x ≥ 60.0)
A random variable is Poisson distributed with λ = 0.50 arrivals per minute. For the corresponding exponential distribution, and x = minutes until the next arrival, identify the mean of x and determine the following: a. P(x ≤ 0.5) b. P(x ≤ 1.5) c. P(x ≥ 2.5) d. P(x ≥ 3.0)
The owner of a self-service car wash has found that customers take an average of 8 minutes to wash and dry their cars. Assuming that the self-service times tend to be exponentially distributed, what is the probability that a customer will require more than 10 minutes to complete the job?
A taxi dispatcher has found that successive calls for taxi service are exponentially distributed, with a mean time between calls of 5.30 minutes. The dispatcher must disconnect the telephone system for 3 minutes in order to have the push-button mechanism repaired. What is the probability that a
During 2008, U.S. general aviation pilots had 1.20 fatal crashes per 100,000 flying hours. Harriet Arnold is president of Arnold’s Flying Service, a company that operates a total of 50 sightseeing planes based in 20 regions of the United States. Altogether, the planes in this fleet are in the air
The Bureau of Labor Statistics reports the fatality rate for workers in the rail transportation industry is 0.006 fatalities per 200,000 worker-hours. During 2007, rail transportation workers put in a total of 545 million worker-hours. Assuming that (1) an exponential distribution applies for the
A computer statistical package has simulated 1000 random observations from a normal distribution with μ = 50 and σ = 10. Sketch the approximate box-and whisker display for the resulting data.
A computer statistical package has simulated 2000 random observations from a normal distribution with μ = 80 and σ = 20. Sketch the approximate box-and whisker display for the resulting data.
If a computer statistical package were to simulate 2000 random observations from a normal distribution with μ = 150 and σ = 25, what percentage of these observations would you expect to have a value of 140 or less? Do you think the actual number in the “#140” range would equal the expected
If a computer statistical package were to simulate 1000 random observations from a normal distribution with μ = 200 and σ = 50, what percentage of these observations would you expect to have a value of 300 or more? Do you think the actual number in the “$300” range would equal the expected
According to a recent survey, 35% of the adult citizens of Mayville have a charge account at Marcy’s Department Store. Mr. Marcy’s nephew is going to trial for embezzlement, and nine jurors are to be randomly selected from the adult citizenry. What is the probability that at least four of the
A food expert claims that there is no difference between the taste of two leading soft drinks. In a taste test involving 200 persons, however, 55% of the subjects say they like soft drink A better than B. If the food expert is correct, we would expect that 50% of the persons would have preferred
In Exercise 7.64, the maker of soft drink A claims its product to be “superior” to soft drink B. Given the results obtained in Exercise 7.64, do they appear to have a solid basis for their claim? In exercise A food expert claims that there is no difference between the taste of two leading soft
During an annual heating season, the average gas bill for customers in a New England community heating their homes with gas was $457. Assuming a normal distribution and a standard deviation of $80:a. What proportion of homes heating with gas had a gas bill over $382?b. What proportion of homes
It has been reported that the average monthly cell phone bill is $50. Assuming a normal distribution and a standard deviation of $10, what is the probability that a randomly selected cell phone subscriber’s bill last month was less than $35? More than $70?
During 2004, the average number of flying hours for aircraft operated by regional airlines in the United States was 2389. Assume a normal distribution and a standard deviation of 300 hours. Source: Statistical Abstract of the United States 2006, p. 701. a. What proportion of aircraft flew more than
During fiscal 2008, the average daily volume for FedEx Corporation was 7,000,000 packages per day. Assuming a normal distribution and a standard deviation of 800,000 packages per day, on what proportion of the days was the volume between 6,000,000 and6,500,000 packages?
For itemized tax returns in the $60,000–$75,000 income group for the most recent year reported, the average charitable contribution was $1935. Assume a normal distribution and a standard deviation of $400.a. For a randomly selected household from this income group, what is the probability that
Of the 1.0 million persons of voting age in Maine, 72% voted in the 2008 presidential election. For a randomly selected group of 30 Maine residents who were of voting age at that time, what is the probability that at least 20 of these persons voted in the presidential election?
A public relations agency tells its client that 80% of the residents in a 50-mile radius believe the company is “an industry leader.” Skeptical, the company commissions a survey in which just 320 of the 500 persons interviewed felt the company was an industry leader. If the public relations
Given the results of Exercise 7.72, evaluate the claim made by the public relations agency. Result A public relations agency tells its client that 80% of the residents in a 50-mile radius believe the company is “an industry leader.”
A researcher is studying a particular process and has identified the following times, in minutes, between consecutive occurrences: 1.8, 4.3, 2.3, 2.1, 5.6, 1.5, 4.5, 1.8, 2.4, 2.6, 3.2, 3.5, 1.6, 2.1, and 1.9. Given this information, what would be the researcher’s best estimate for the mean of
A safety researcher has found that fourth to sixth graders engaging in unorganized activities on school grounds experienced injuries at the rate of 2.4 injuries per 100 thousand student-days. On the average, how many student-days elapse between injuries to fourth to sixth graders in unorganized
The number of defects in rolls of aluminum sheet average 3.5 defects per 100 feet. The company president is accompanying overseas visitors on a tour of the plant, and they have just arrived at the aluminum-sheet machine. If they remain at the machine long enough to observe 32 feet of aluminum being
The mileage death rate for motorcycle riders has been estimated to be about 39 deaths per 100 million miles of motorcycle travel. A national motorcycling association has 1200 members who travel a total of 2 million miles each year on their motorcycles. What is the probability that the next highway
The “20-ounce” package of mozzarella cheese distributed by a food company actually has a weight that is normally distributed, with μ = 21 ounces and σ = 0.2 ounces.a. What is the probability that a randomly selected package of this cheese will actually contain at least 20.5 ounces?b. What is
State Police Academy graduates from a large graduating class have scored an average of 81.0 on a proficiency test, and the scores are normally distributed with σ = 8.5. Graduates are randomly paired and assigned to barracks throughout the state. Madeleine has scored 83.0 on the test. What is the
If x is normally distributed with μ = 20.0 and σ = 4.0, determine the following: a. P(x ≥ 20.0) b. P(16.0 ≤ x ≤ 24.0) c. P(x ≤ 12) d. P(x = 22.0) e. P(12.0 ≤ x ≤ 28.0) f. P(x ≥ 16)
The trainer for a professional football team has found that, on the average, his team experiences 2.3 sprained ankles per 1000 game minutes. If a game lasts 60 minutes, and the number of game minutes between ankle sprains is exponentially distributed, determine the probability that the next ankle
The precooked weight of hamburgers at a gourmet hamburger restaurant has been normally distributed with a mean of 5.5 ounces and a standard deviation of 0.15 ounces. A dining-column journalist from the local newspaper enters the restaurant and orders a hamburger. What is the probability that he
Boxes are filled with sugar by a machine that is set to deliver an average of 20.3 ounces. The weights are normally distributed with a standard deviation of 0.3 ounces. If a consumer advocate buys a package of the product and then proceeds to weigh the contents, what is the probability that the
In Exercise 7.82, the company would like to put in a greater weight “cushion” to help protect itself from consumer advocates. If the company wants to have just 2% of the packages contain less than 20 ounces, to what average weight must the filling machine be set? In exercise Boxes are filled
Discount Micros, a computer mail-order company, has received 2000 desktop computers from a major manufacturer. Unknown to the mail-order company, 250 of the computers have a hard disk that was improperly installed at the factory. A consulting firm purchases 40 computers from Discount Micros. If the
The U-Drive car rental corporation has found that the cars in the company’s rental fleet experience punctures at the rate of 1.25 punctures per 10,000 miles, and the number of punctures per distance traveled is Poisson distributed. Ed and Harriet are taking advantage of a U-Drive promotion in
Bonnie Rogers, the customer relations manager for a large computer manufacturer, has recently studied the duration of telephone calls received by the company’s technical support department. The call lengths are exponentially distributed, with a mean duration of 8 minutes. Experience has taught
A storage warehouse in a relatively remote part of a county is protected by a homemade burglary detection system. Once actuated by an intruder, the system sounds a horn and flashes a light for 15 minutes, then saves battery power by shutting down and resetting itself until the next intrusion is
If x is normally distributed with μ = 25.0 and σ = 5.0, determine the following: a. P(x ≥ 25.0) b. P(20.0 ≤ x ≤ 30.0) c. P(x ≤ 30) d. P(x = 26.2) e. P(15.0 ≤ x ≤ 25.0) f. P(x ≥ 15)
Since Thorndike “Graph-Pro” racquetball racquets were introduced several years ago, no attempt has ever been made to offer a lightweight version. Ted has done some research and found that some of the other manufacturers offer a lighter version of their standard racquet. In addition, some of the
During an 8-hour shift of golf-ball production, one golf ball is randomly selected from each 2 minutes’ worth of output. The ball is then tested for “liveliness” by rolling it down a grooved, stainless- steel surface. At the bottom, it strikes a smooth iron block and bounces backward, up a
What is the difference between a probability distribution and a sampling distribution?
Employees in a large manufacturing plant worked an average of 62.0 hours of overtime last year, with a standard deviation of 15.0 hours. For a simple random sample of n = 36 employees and x = the number of overtime hours worked last year, determine the z-score corresponding to each of the following
For the manufacturing plant discussed in Exercise 8.10, the union president and the human resources director jointly select a simple random sample of 36 employees to engage in a discussion with regard to the company’s work rules and overtime policies. What is the probability that the average
Shirley Johnson, a county political leader, is looking ahead to next year’s election campaign and the possibility that she might be forced to support a property tax increase to help combat projected shortfalls in the county budget. For the dual purpose of gaining voter support and finding out
An industrial crane is operated by four electric motors working together. For the crane to perform properly, the four motors have to generate a total of at least 380 horsepower. Engineers from the plant that produces the electric motors have stated that motors off their assembly line average 100
From past experience, an airline has found the luggage weight for individual air travelers on its trans- Atlantic route to have a mean of 80 pounds and a standard deviation of 20 pounds. The plane is consistently fully booked and holds 100 passengers. The pilot insists on loading an extra 500
A hardware store chain has just received a truckload of 5000 electric drills. Before accepting the shipment, the purchasing manager insists that 9 of the drills be randomly selected for testing. He intends to measure the maximum power consumption of each drill and reject the shipment if the mean
The tensile strength of spot welds produced by a robot welder is normally distributed, with a mean of 10,000 pounds per square inch and a standard deviation of 800 pounds per square inch. For a simple random sample of n = 4 welds, what is the probability that the sample mean will be at least 10,200
At a department store catalog orders counter, the average time that a customer has to wait before being served has been found to be approximately exponentially distributed, with a mean (and standard deviation) of 3.5 minutes. For a simple random sample of 36 recent customers, invoke the central
It has been reported that the average U.S. teenager sends 80 text messages per day. For purposes of this exercise, we will assume the daily number of text messages sent is normally distributed with a standard deviation of 15.0 messages. For a randomly selected group of 10 teenagers, and considering
The average length of a hospital stay in general or community hospitals in the United States is 5.5 days. Assuming a population standard deviation of 2.5 days and a simple random sample of 50 patients, what is the probability that the average length of stay for this group of patients will be no
According to the Newspaper Association of America, the average visitor to online newspaper sites spends 45 minutes per month reading online news content. Assuming a population standard deviation of 10 minutes and a simple random sample of 30 online newspaper readers, what is the probability that
According to the Federal Reserve System, 46% of U.S. households have credit-card debt. For simple random samples of size n, with n > 30, describe the sampling distribution of p = the proportion of households in the sample who have credit-card debt.
Shirley Johnson, the county political leader discussed in Exercise 8.12, is a Republican. According to voter registration records, 60% of the homeowners in her county are also Republicans. For the simple random sample of 40 homeowners invited to attend her town meeting, describe the sampling
A simple random sample with n = 300 is drawn from a binomial process in which π = 0.4. Determine the following probabilities for p = the proportion of successes: a. P(p ≥ 0.35) b. P(0.38 ≤ p ≤ 0.42) c. P(p ≤ 0.45)
A simple random sample with n = 200 is drawn from a binomial process in which π = 0.6. Determine the following probabilities for p = the proportion of successes:a. P (0.50 ≤ p)b. P (0.65 ≤ p ≤ 0.70)c. P (p $ 0.70)
It has been reported that 40% of U.S. workers employed as purchasing managers are females. In a simple random sample of U.S. purchasing managers, 70 out of the 200 are females. Given this information: a. What is the population proportion, π? b. What is the sample proportion, p? c. What is the
According to the Investment Company Institute, 40% of U.S. households have an Individual Retirement Account (IRA). Assuming the population proportion to be π = 0.40 and that a simple random sample of 400 households has been selected:a. What is the expected value of p = the proportion in the sample

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