A uniform distribution is defined over the interval from 2 to 5. a. What are the values

A uniform distribution is defined over the interval from 6 to 10. a. What are the values for a and b? b. What is the mean of this uniform distribution? c. What is the standard deviation? d. Show that the total area is 1.00. e. Find the probability of a value more than 7. f. Find the probability of a value between 7 and 9.

A uniform distribution is defined over the interval from 2 to 5. a. What are the values for a and b? b. What is the mean of this uniform distribution? c. What is the standard deviation? d. Show that the total area is 1.00. e. Find the probability of a value more than 2.6. f. Find the probability of a value between 2.9 and 3.7.

The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and 30 per share. What is the probability that the stock price will be: a. More than $27? b. Less than or equal to $24?

According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts. a. What is the mean amount spent on insurance? b. What is the standard deviation of the amount spent? c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? d. What is the probability a family spends more than $3,000 per year?

The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. a. What are the values for a and b? b. What is the mean amount of rainfall for the month? What is the standard deviation? c. What is the probability of less than an inch of rain for the month? d. What is the probability of exactly 1.00 inch of rain? e. What is the probability of more than 1.50 inches of rain for the month?

Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds to 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution. a. What are the values for a and b in minutes? b. What is the mean time to resolve the problem? What is the standard deviation of the time? c. What percent of the problems take more than 5 minutes to resolve? d. Suppose we wish to find the middle 50 percent of the problem-solving times. What are the end points of these two times?

Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds to 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution. a. What are the values for a and b in minutes? b. What is the mean time to resolve the problem? What is the standard deviation of the time? c. What percent of the problems take more than 5 minutes to resolve? d. Suppose we wish to find the middle 50 percent of the problem-solving times. What are the end points of these two times?

List the major characteristics of a normal probability distribution.

The mean of a normal probability distribution is 500; the standard deviation is 10. a. About 68 percent of the observations lie between what two values? b. About 95 percent of the observations lie between what two values? c. Practically all of the observations lie between what two values?

The mean of a normal probability distribution is 60; the standard deviation is 5. a. About what percent of the observations lie between 55 and 65? b. About what percent of the observations lie between 50 and 70? c. About what percent of the observations lie between 45 and 75?

The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $50,000 per year. Rachel works in the retail industry, where the mean salary for executives with less than 5 years experience is $35,000 with a standard deviation of $8,000. Rob is an engineer. The mean salary for engineers with less than 5 years experience is $60,000 with a standard deviation of $5,000. Compute the z values for both Rob and Rachel and comment on your findings

A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Montes Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal probability distribution. Compute z values for each and comment on your findings

A normal population has a mean of 20.0 and a standard deviation of 4.0. a. Compute the z value associated with 25.0. b. What proportion of the population is between 20.0 and 25.0? c. What proportion of the population is less than 18.0?

A normal population has a mean of 12.2 and a standard deviation of 2.5. a. Compute the z value associated with 14.3. b. What proportion of the population is between 12.2 and 14.3? c. What proportion of the population is less than 10.0?

A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50. Assume the distribution of hourly wages follows the normal probability distribution. If we select a crew member at random, what is the probability the crew member earns: a. Between $20.50 and $24.00 per hour? b. More than $24.00 per hour? c. Less than $19.00 per hour?

The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? b. What is the area between the mean and 395 pounds? c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

A normal distribution has a mean of 50 and a standard deviation of 4. a. Compute the probability of a value between 44.0 and 55.0. b. Compute the probability of a value greater than 55.0. c. Compute the probability of a value between 52.0 and 55.0

A normal population has a mean of 80.0 and a standard deviation of 14.0. a. Compute the probability of a value between 75.0 and 90.0. b. Compute the probability of a value 75.0 or less. c. Compute the probability of a value between 55.0 and 70.0.

According to the Internal Revenue Service, the mean tax refund for the year 2007 was $2,708. Assume the standard deviation is $650 and that the amounts refunded follow a normal probability distribution. a. What percent of the refunds are more than $3,000? b. What percent of the refunds are more than $3,000 but less than $3,500? c. What percent of the refunds are more than $2,500 but less than $3,500?

The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next weeks show will: a. Have between 30 and 34 million viewers? b. Have at least 23 million viewers? c. Exceed 40 million viewers?

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in: a. More than 20 minutes? b. For 20 minutes or less? c. Between 10 and 12 minutes?

Among U.S. cities with a population of more than 250,000, the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 38.3 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.5 minutes. a. What percent of the New York City commutes are for less than 30 minutes? b. What percent are between 30 and 35 minutes? c. What percent are between 30 and 40 minutes?

A normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95 percent of the observations will occur

A normal distribution has a mean of 80 and a standard deviation of 14. Determine the value above which 80 percent of the values will occur

Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,100 per hour and a standard deviation of $250. What is the operating cost for the lowest 3 percent of the airplanes?

The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for college admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top 10 percent of this test. What is the minimum score that qualifies for the scholarship?

According to media research, the typical American listened to 195 hours of music in the last year. This is down from 290 hours four years earlier. Dick Trythall is a big country and western music fan. He listens to music while working around the house, reading, and riding in his truck. Assume the number of hours spent listening to music follows a normal probability distribution with a standard deviation of 8.5 hours. a. If Dick is in the top 1 percent in terms of listening time, how many hours does he listen per year? b. Assume that the distribution of times four years earlier also follows the normal probability distribution with a standard deviation of 8.5 hours. How many hours did the 1 percent who listen to the least music actually listen?

For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500. Ninety-five percent of all students at private universities pay less than what amount?

In economic theory, a hurdle rate is the minimum return that a person requires before they will make an investment. A research report says that annual returns from a specific class of common equities are distributed according to a normal distribution with a mean of 12 percent and a standard deviation of 18 percent. A stock screener would like to identify a hurdle rate such that only 1 in 20 equities is above that value. Where should the hurdle rate be set?

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,200. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 820 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. How many pages should the manufacturer advertise for each cartridge if it wants to be correct 99 percent of the time?

Assume a binomial probability distribution with n 50 and  .25. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that X is 15 or more. c. The probability that X is 10 or less.

Assume a binomial probability distribution with n 40 and  .55. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that X is 25 or greater. c. The probability that X is 15 or less. d. The probability that X is between 15 and 25, inclusive.

Dotties Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 7 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 80 returns, what is the probability that she makes errors on: a. More than six returns? b. At least six returns? c. Exactly six returns?

Shortys Muffler advertises it can install a new muffler in 30 minutes or less. However, the work standards department at corporate headquarters recently conducted a study and found that 20 percent of the mufflers were not installed in 30 minutes or less. The Maumee branch installed 50 mufflers last month. If the corporate report is correct: a. How many of the installations at the Maumee branch would you expect to take more than 30 minutes? b. What is the likelihood that fewer than eight installations took more than 30 minutes? c. What is the likelihood that eight or fewer installations took more than 30 minutes? d. What is the likelihood that exactly 8 of the 50 installations took more than 30 minutes?

A study conducted by the nationally known Taurus Health Club revealed that 30 percent of its new members are significantly overweight. A membership drive in a metropolitan area resulted in 500 new members. a. It has been suggested that the normal approximation to the binomial be used to determine the probability that 175 or more of the new members are significantly overweight. Does this problem qualify as a binomial problem? Explain. b. What is the probability that 175 or more of the new members are significantly overweight? c. What is the probability that 140 or more new members are significantly overweight?

A recent issue of Bride Magazine suggested that couples planning their wedding should expect two-thirds of those who are sent an invitation to respond that they will attend. Rich and Stacy are planning to be married later this year. They plan to send 197 invitations. a. How many guests would you expect to accept the invitation? b. What is the standard deviation? c. What is the probability 140 or more will accept the invitation? d. What is the probability exactly 140 will accept the invitation?

Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a mean of 60 seconds. Calculate the probability a customer waits: a. Less than 30 seconds. b. More than 120 seconds. c. Between 45 and 75 seconds. d. Fifty percent of the patrons wait less than how many seconds? What is the median?

The lifetime of plasma and LCD TV sets follows an exponential distribution with a mean of 100,000 hours. Compute the probability a television set: a. Fails in less than 10,000 hours. b. Lasts more than 120,000 hours. c. Fails between 60,000 and 100,000 hours of use. d. Find the 90th percentile. So 10 percent of the TV sets last more than what length of time?

The Bureau of Labor Statistics American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged 0.3 hour (18 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.0 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends: a. Less than 15 minutes per day using a computer for leisure. b. More than two hours. c. Between 30 minutes and 90 minutes using a computer for leisure. d. Find the 20th percentile. Eighty percent spend more than what amount of time?

The cost per item at a supermarket follows an exponential distribution. There are many inexpensive items and a few relatively expensive ones. The mean cost per item is $3.50. What is the percentage of items that cost: a. Less than $1? b. More than $4? c. Between $2 and $3? d. Find the 40th percentile. Sixty percent of the supermarket items cost more than what amount?

The amount of cola in a 12-ounce can is uniformly distributed between 11.96 ounces and 12.05 ounces. a. What is the mean amount per can? b. What is the standard deviation amount per can? c. What is the probability of selecting a can of cola and finding it has less than 12 ounces? d. What is the probability of selecting a can of cola and finding it has more than 11.98 ounces? e. What is the probability of selecting a can of cola and finding it has more than 11.00 ounces?

A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the toothpaste, the amount remaining in any tube is random. Assume the amount of toothpaste left in the tube follows a uniform distribution. From this information, we can determine the following information about the amount remaining in a toothpaste tube without invading anyones privacy. a. How much toothpaste would you expect to be remaining in the tube? b. What is the standard deviation of the amount remaining in the tube? c. What is the likelihood there is less than 3.0 ounces remaining in the tube? d. What is the probability there is more than 1.5 ounces remaining in the tube?

Many retail stores offer their own credit cards. At the time of the credit application, the customer is given a 10 percent discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes. a. What is the mean time for the application process? b. What is the standard deviation of the process time? c. What is the likelihood a particular application will take less than 6 minutes? d. What is the likelihood an application will take more than 5 minutes?

The time patrons at the Grande Dunes Hotel in the Bahamas spend waiting for an elevator follows a uniform distribution between 0 and 3.5 minutes. a. Show that the area under the curve is 1.00. b. How long does the typical patron wait for elevator service? c. What is the standard deviation of the waiting time? d. What percent of the patrons wait for less than a minute? e. What percent of the patrons wait more than 2 minutes?

The net sales and the number of employees for aluminum fabricators with similar characteristics are organized into frequency distributions. Both are normally distributed. For the net sales, the mean is $180 million and the standard deviation is $25 million. For the number of employees, the mean is 1,500 and the standard deviation is 120. Clarion Fabricators had sales of $170 million and 1,850 employees. a. Convert Clarions sales and number of employees to z values. b. Locate the two z values. c. Compare Clarions sales and number of employees with those of the other fabricators

The accounting department at Weston Materials Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect? b. What percent of the garages take between 29 hours and 34 hours to erect?

A recent report in USA Today indicated a typical family of four spends $490 per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a mean of $490 and a standard deviation of $90. a. What percent of the families spend more than $30 but less than $490 per month on food? b. What percent of the families spend less than $430 per month on food? c. What percent spend between $430 and $600 per month on food? d. What percent spend between $500 and $600 per month on food?

A study of long-distance phone calls made from General Electric revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes. a. What fraction of the calls last between 4.2 and 5 minutes? b. What fraction of the calls last more than 5 minutes? c. What fraction of the calls last between 5 and 6 minutes? d. What fraction of the calls last between 4 and 6 minutes? e. As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4 percent of the calls. What is this time?

Shaver Manufacturing Inc. offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal probability distribution, with a mean of $1,280 and a standard deviation of $420 per year. a. What fraction of the employees cost more than $1,500 per year for dental expenses? b. What fraction of the employees cost between $1,500 and $2,000 per year? c. Estimate the percent that did not have any dental expense. d. What was the cost for the 10 percent of employees who incurred the highest dental expense?

The annual commissions earned by sales representatives of Machine Products Inc., a manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5,000. a. What percent of the sales representatives earn more than $42,000 per year? b. What percent of the sales representatives earn between $32,000 and $42,000? c. What percent of the sales representatives earn between $32,000 and $35,000? d. The sales manager wants to award the sales representatives who earn the largest commissions a bonus of $1,000. He can award a bonus to 20 percent of the representatives. What is the cutoff point between those who earn a bonus and those who do not?

According to the South Dakota Department of Health, the mean number of hours of TV viewing per week is higher among adult women than men. A recent study showed women spent an average of 34 hours per week watching TV and men 29 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.5 hours and is 5.1 hours for the men. a. What percent of the women watch TV less than 40 hours per week? b. What percent of the men watch TV more than 25 hours per week? c. How many hours of TV do the one percent of women who watch the most TV per week watch? Find the comparable value for the men.

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,994. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $450. a. What percent of the adults spend more than $2,500 per year on reading and entertainment? b. What percent spend between $2,500 and $3,000 per year on reading and entertainment? c. What percent spend less than $1,000 per year on reading and entertainment?

Management at Gordon Electronics is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate weekly production follows the normal distribution. The mean of this distribution is 4,000 units per week and the standard Lin01803_ch07_222-264.qxd 10/23/10 12:34 PM Page 253 254 Chapter 7 deviation is 60 units per week. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more?

Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles. a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more? b. What percent of the trucks logged more than 57,060 but less than 58,280 miles? c. What percent of the Fords traveled 62,000 miles or less during the year? d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? Explain

Best Electronics Inc. offers a no hassle returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.3 per day and the standard deviation is 2.25 per day. a. In what percent of the days are there 8 or fewer customers returning items? b. In what percent of the days are between 12 and 14 customers returning items? c. Is there any chance of a day with no returns?

A recent report in BusinessWeek indicated that 20 percent of all employees steal from their company each year. If a company employs 50 people, what is the probability that: a. Fewer than 5 employees steal? b. More than 5 employees steal? c. Exactly 5 employees steal? d. More than 5 but fewer than 15 employees steal?

The Orange County Register, as part of its Sunday health supplement, reported that 64 percent of American men over the age of 18 consider nutrition a top priority in their lives. Suppose we select a sample of 60 men. What is the likelihood that: a. 32 or more consider nutrition important? b. 44 or more consider nutrition important? c. More than 32 but fewer than 43 consider nutrition important? d. Exactly 44 consider diet important?

It is estimated that 10 percent of those taking the quantitative methods portion of the CPA examination fail that section. Sixty students are taking the exam this Saturday. a. How many would you expect to fail? What is the standard deviation? b. What is the probability that exactly two students will fail? c. What is the probability at least two students will fail?

The Georgetown, South Carolina, Traffic Division reported 40 percent of high-speed chases involving automobiles result in a minor or major accident. During a month in which 50 high-speed chases occur, what is the probability that 25 or more will result in a minor or major accident?

Cruise ships of the Royal Viking line report that 80 percent of their rooms are occupied during September. For a cruise ship having 800 rooms, what is the probability that 665 or more are occupied in September?

The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Lets interpret this to mean that 95 percent of the flights are cleared in 45 minutes, so 5 percent of the flights take longer to clear. Lets also assume that the distribution is approximately normal. a. If the standard deviation of the time to clear an international flight is 5 minutes, what is the mean time to clear a flight? b. Suppose the standard deviation is 10 minutes, not the 5 minutes suggested in part (a). What is the new mean? c. A customer has 30 minutes from the time her flight lands to catch her limousine. Assuming a standard deviation of 10 minutes, what is the likelihood that she will be cleared in time?

The funds dispensed at the ATM machine located near the checkout line at the Krogers in Union, Kentucky, follows a normal probability distribution with a mean of $4,200 per day and a standard deviation of $720 per day. The machine is programmed to notify the nearby bank if the amount dispensed is very low (less than $2,500) or very high (more than $6,000). a. What percent of the days will the bank be notified because the amount dispensed is very low? b. What percent of the time will the bank be notified because the amount dispensed is high? c. What percent of the time will the bank not be notified regarding the amount of funds dispersed?

The weights of canned hams processed at Henline Ham Company follow the normal distribution, with a mean of 9.20 pounds and a standard deviation of 0.25 pounds. The label weight is given as 9.00 pounds. a. What proportion of the hams actually weigh less than the amount claimed on the label? b. The owner, Glen Henline, is considering two proposals to reduce the proportion of hams below label weight. He can increase the mean weight to 9.25 and leave the standard deviation the same, or he can leave the mean weight at 9.20 and reduce the standard deviation from 0.25 pounds to 0.15. Which change would you recommend?

The Cincinnati Enquirer, in its Sunday business supplement, reported that the mean number of hours worked per week by those employed full time is 43.9. The article further indicated that about one-third of those employed full time work less than 40 hours per week. a. Given this information and assuming that number of hours worked follows the normal distribution, what is the standard deviation of the number of hours worked? b. The article also indicated that 20 percent of those working full time work more than 49 hours per week. Determine the standard deviation with this information. Are the two estimates of the standard deviation similar? What would you conclude?

Most four-year automobile leases allow up to 60,000 miles. If the lessee goes beyond this amount, a penalty of 20 cents per mile is added to the lease cost. Suppose the distribution of miles driven on four-year leases follows the normal distribution. The mean is 52,000 miles and the standard deviation is 5,000 miles. a. What percent of the leases will yield a penalty because of excess mileage? b. If the automobile company wanted to change the terms of the lease so that 25 percent of the leases went over the limit, where should the new upper limit be set? c. One definition of a low-mileage car is one that is 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage?

The price of shares of Bank of Florida at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share. a. What percent of the days was the price over $45.00? How many days would you estimate? b. What percent of the days was the price between $38.00 and $40.00? c. What was the stocks price on the highest 15 percent of days?

The annual sales of romance novels follow the normal distribution. However, the mean and the standard deviation are unknown. Forty percent of the time sales are more than 470,000, and 10 percent of the time sales are more than 500,000. What are the mean and the standard deviation?

In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at the manufacturers expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV, the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturers expense?

DeKorte Tele-Marketing Inc. is considering purchasing a machine that randomly selects and automatically dials telephone numbers. DeKorte Tele-Marketing makes most of its calls during the evening, so calls to business phones are wasted. The manufacturer of the machine claims that its programming reduces the calling to business phones to 15 percent of all calls. To test this claim, the director of purchasing at DeKorte programmed the machine to select a sample of 150 phone numbers. What is the likelihood that more than 30 of the phone numbers selected are those of businesses, assuming the manufacturers claim is correct?

DeKorte Tele-Marketing Inc. is considering purchasing a machine that randomly selects and automatically dials telephone numbers. DeKorte Tele-Marketing makes most of its calls during the evening, so calls to business phones are wasted. The manufacturer of the machine claims that its programming reduces the calling to business phones to 15 percent of all calls. To test this claim, the director of purchasing at DeKorte programmed the machine to select a sample of 150 phone numbers. What is the likelihood that more than 30 of the phone numbers selected are those of businesses, assuming the manufacturers claim is correct?

Boot Time (the time between the appearance of the Bios screen to the first file that is loaded in Windows) on Eric Mousers personal computer follows an exponential distribution with a mean of 27 seconds. What is the probability his boot will require: a. Less than 15 seconds? b. More than 60 seconds? Lin01803_ch07_222-264.qxd 10/23/10 12:34 PM Page 255 256 Chapter 7 c. Between 30 and 45 seconds? d. What is the point below which only 10 percent of the boots occur?

The time between visits to a U.S. emergency room for a member of the general population follows an exponential distribution with a mean of 2.5 years. What proportion of the population will visit an emergency room: a. Within the next six months? b. Not visit the ER over the next six years? c. Next year, but not this year? d. Find the first and third quartiles of this distribution.

The times between failures on a personal computer follow an exponential distribution with a mean of 300,000 hours. What is the probability of: a. A failure in less than 100,000 hours? b. No failure in the next 500,000 hours? c. The next failure occurring between 200,000 and 350,000 hours? d. What are the mean and standard deviation of the time between failures?

Refer to the Real Estate data, which report information on homes sold in the Goodyear, Arizona, area during the last year. a. The mean selling price (in $ thousands) of the homes was computed earlier to be $221.10, with a standard deviation of $47.11. Use the normal distribution to estimate the percentage of homes selling for more than $280.0. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results? b. The mean distance from the center of the city is 14.629 miles, with a standard deviation of 4.874 miles. Use the normal distribution to estimate the number of homes 18 or more miles but less than 22 miles from the center of the city. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results?

Refer to the Baseball 2009 data, which report information on the 30 Major League Baseball teams for the 2009 season. a. The mean attendance per team for the season was 2.448 million, with a standard deviation of 0.698 million. Use the normal distribution to estimate the number of teams with attendance of more than 3.5 million. Compare that estimate with the actual number. Comment on the accuracy of your estimate. b. The mean team salary was $88.51 million, with a standard deviation of $33.90 million. Use the normal distribution to estimate the number of teams with a team salary of more than $50 million. Compare that estimate with the actual number. Comment on the accuracy of the estimate

Refer to the Buena School District bus data. a. Refer to the maintenance cost variable. The mean maintenance cost for last year is $450.29, with a standard deviation of 53.69. Estimate the number of buses with a cost of more than $500. Compare that with the actual number. b. Refer to the variable on the number of miles driven. The mean is 830.11 and the standard deviation is 42.19 miles. Estimate the number of buses traveling more than 900 miles. Compare that number with the actual value.