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theory of statistics

Basic Statistics For Business And Economics 6th Edition Douglas Lind, William Marchal, Samuel Wathen - Solutions

What is sampling error? Could the value of the sampling error be zero? If it were zero, what would this mean?
Medical Mutual Insurance is investigating the cost of a routine office visit to family- practice physicians in the Rochester, New York, area. The following is a list of family-practice physicians in the region. Physicians are to be randomly selected and contacted regarding their charges. The 39
The retail stores located in the North Towne Square Mall are:a. If the following random numbers are selected, which retail stores should be contacted for a survey? 11, 65, 86, 62, 06, 10, 12, 77, and 04.b. Select a random sample of four retail stores. Use Appendix B.6.c. A systematic sampling
According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form.This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40
The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of $250 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the
A normal population has a mean of 75 and a standard deviation of 5.You select a sample of 40. Compute the probability the sample mean is:a. Less than 74.b. Between 74 and 76.c. Between 76 and 77.d. Greater than 77.
A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is:a. Greater than 63.b. Less than 56.c. Between 56 and 63.
Refer to the Cola, Inc., information. Suppose the quality technician selected a sample of 16 Jumbo bottles that averaged 31.08 ounces.What can you conclude about the filling process?
The Quality Assurance Department for Cola, Inc., maintains records regarding the amount of cola in its Jumbo bottle. The actual amount of cola in each bottle is critical, but varies a small amount from one bottle to the next. Cola, Inc., does not wish to underfill the bottles, because it will have
Haughton Elevator Company wishes to develop specifications for the number of people who can ride in a new oversized elevator. Suppose the mean weight for an adult is 160 pounds and the standard deviation is 15 pounds. However, the distribution of weights does not follow the normal probability
A. C. Nielsen Company provides information to companies advertising on television. Prior research indicates that adult Americans watch an average of 6.0 hours per day of television. The standard deviation is 1.5 hours. For a sample of 50 adults in the greater Boston area, would it be reasonable
Arm and Hammer Company wants to ensure that its laundry detergent actually contains 100 fluid ounces, as indicated on the label. Historical summaries from the filling process indicate the mean amount per container is 100 fluid ounces and the standard deviation is 2 fluid ounces. The quality
Consider the digits in the phone numbers on a randomly selected page of your local phone book a population. Make a frequency table of the final digit of 30 randomly selected phone numbers. For example, if a phone number is 555-9704, record a 4.a. Draw a histogram or other graph of this population
Consider all of the coins (pennies, nickels, quarters, etc.) in your pocket or purse as a population. Make a frequency table beginning with the current year and counting backward to record the ages (in years) of the coins. For example, if the current year is 2007, then a coin with 2004 stamped on
Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population valuesa. Draw a graph showing the population
Appendix B.6 is a table of random numbers. Hence, each digit from 0 to 9 has the same likelihood of occurrence.a. Draw a graph showing the population distribution. What is the population mean?b. Following are the first 10 rows of five digits from Appendix B.6.Assume that these are 10 random samples
Refer to the Spence Sprockets, Inc., data here. Select 10 random samples of 5 employees each. Use the methods described earlier in the chapter and the Table of Random Numbers (Appendix B.6) to find the employees to include in the sample. Compute the mean of each sample and plot the sample means on
Ed Spence began his sprocket business 20 years ago. The business has grown over the years and now employs 40 people. Spence Sprockets, Inc., faces some major decisions regarding health care for these employees. Before making a final decision on what health care plan to purchase, Ed decides to form
There are five sales associates at Mid-Motors Ford. The five representatives and the number of cars they sold last week are:a. How many different samples of size 2 are possible?b. List all possible samples of size 2, and compute the mean of each sample.c. Compare the mean of the sampling
In the law firm Tybo and Associates, there are six partners. Listed below is the number of cases each associate actually tried in court last month.a. How many different samples of 3 are possible?b. List all possible samples of size 3, and compute the mean number of cases in each sample.c. Compare
A population consists of the following five values: 0, 0, 1, 3, 6.a. List all samples of size 3, and compute the mean of each sample.b. Compute the mean of the distribution of sample means and the population mean. Compare the two values.c. Compare the dispersion in the population with that of the
A population consists of the following five values: 12, 12, 14, 15, and 20.a. List all samples of size 3, and compute the mean of each sample.b. Compute the mean of the distribution of sample means and the population mean. Compare the two values.c. Compare the dispersion in the population with that
A population consists of the following five values: 2, 2, 4, 4, and 8.a. List all samples of size 2, and compute the mean of each sample.b. Compute the mean of the distribution of sample means and the population mean. Compare the two values.c. Compare the dispersion in the population with that of
A population consists of the following four values: 12, 12, 14, and 16.a. List all samples of size 2, and compute the mean of each sample.b. Compute the mean of the distribution of the sample mean and the population mean. Compare the two values.c. Compare the dispersion in the population with that
The lengths of service of all the executives employed by Standard Chemicals are:(a) Using the combination formula, how many samples of size 2 are possible?(b) List all possible samples of 2 executives from the population and compute their means.(c) Organize the means into a sampling
Tartus Industries has seven production employees (considered the population). The hourly earnings of each employee are given in Table 8–2.1. What is the population mean?2. What is the sampling distribution of the sample mean for samples of size 2?3. What is the mean of the sampling
Listed below are the 27 Nationwide Insurance agents in the Toledo, Ohio, metropolitan area. We would like to estimate the mean number of years employed with Nationwide.a. We want to select a random sample of four agents. The random numbers are: 02, 59, 51, 25, 14, 29, 77, 69, and 18. Which dealers
Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments.a. We want to select a random sample of five dealers. The random numbers are:05,20, 59,21,31,28,49,38,66,
The following is a list of hospitals in the Cincinnati (Ohio) and Northern Kentucky Region. Also included is whether the hospital is a general medical/surgical hospital (M/S) or a specialty hospital (S).We are interested in estimating the average number of full- and parttime nurses employed in the
The following is a list of Marco’s Pizza stores in Lucas County. Also noted is whether the store is corporate-owned (C) or manager-owned(M). A sample of four locations is to be selected and inspected for customer convenience, safety, cleanliness, and other features.a. The random numbers selected
Refer to Self-Review 8–1 and the class roster here. Suppose a systematic random sample will select every ninth student enrolled in the class. Initially, the fourth student on the list was selected at random.That student is numbered 03. Remembering that the random numbers start with 00, which
The following class roster lists the students enrolling in an introductory course in business statistics. Three students are to be randomly selected and asked various questions regarding course content and method of instruction.(a) The numbers 00 through 45 are handwritten on slips of paper and
Jane and Joe Miley operate the Foxtrot Inn, a bed and breakfast in Tryon, North Carolina. There are eight rooms available for rent at this B&B. Listed below is the number of these eight rooms rented each day during June 2007. Use Excel to select a sample of five nights during the month of June.
Define and construct a sampling distribution of the sample mean
Describe methods to select a sample.
Explain why a sample is often the only feasible way to learn something about a population.
Refer to the CIA data, which report demographic and economic information on 46 countries.a. The mean of the GDP/capita variable is 16.58 with a standard deviation of 9.27. Use the normal distribution to estimate the percentage of countries with exports above 24. Compare this estimate with the
Refer to the Baseball 2006 data, which report information on the 30 Major League Baseball teams for the 2006 season.a. The mean attendance per team for the season was 2,533,254 with a standard deviation of 706,601. Use the normal distribution to estimate the number of teams with attendance of more
Refer to the Real Estate data, which report information on homes sold in the Denver, Colorado, 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
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?
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
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
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
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
The funds dispensed at the ATM machine located near the checkout line at the Kroger’s 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
The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Let’s 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. Let’s also assume that the distribution is approximately
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.
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
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$2,130 (www.infoplease.com/ipa/ A0908759.html). Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of
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
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
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
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
A study of long-distance phone calls made from the corporate offices of Pepsi Bottling Group, Inc., in Somers, New York, 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
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.
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
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
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
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
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
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
The newsstand at the corner of East 9th Street and Euclid Avenue in downtown Cleveland sells the daily edition of the Cleveland Plain Dealer. The number of papers sold each day follows a normal probability distribution with a mean of 200 copies and a standard deviation of 17 copies.How many copies
In 2006–2007 the mean annual cost to attend a private university in the United States was $22,218. Assume the distribution of annual costs follows a normal probability distribution and the standard deviation is $4,500. Ninetyfive percent of all students at private universities pay less than what
According to media research, the typical American listened to 195 hours of music in the year 2007. This is down from 290 hours in 1999. 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
The monthly sales of mufflers in the Richmond, Virginia, area follow the normal distribution with a mean of 1,200 and a standard deviation of 225.The manufacturer would like to establish inventory levels such that there is only a 5 percent chance of running out of stock. Where should the
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?
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
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.
An analysis of the final test scores for Introduction to Business reveals the scores follow the normal probability distribution. The mean of the distribution is 75 and the standard deviation is 8. The professor wants to award an A to students whose score is in the highest 10 percent. What is the
Layton Tire and Rubber Company wishes to set a minimum mileage guarantee on its new MX100 tire. Tests reveal the mean mileage is 67,900 with a standard deviation of 2,050 miles and that the distribution of miles follows the normal probability distribution. Layton wants to set the minimum guaranteed
Among U.S. cities with a population of more than 250,000 the mean oneway commute 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
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
The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $70,000 and a standard deviation of $20,000. A loan application is received this morning.What is the probability:a. The amount requested is $80,000 or more?b. The
According to the Internal Revenue Service, the mean tax refund for the year 2006 was $2,290. 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
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.
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.
Refer to the previous example, where the distribution of weekly incomes follows the normal distribution with a mean of $1,000 and the standard deviation is $100.(a) What fraction of the shift foremen earn a weekly income between$750 and $1,225? Draw a normal curve and shade the desired area on your
Returning to the weekly income distribution of shift foremen in the glass industry (μ =$1,000, σ =$100), what is the area under the normal curve between $1,150 and $1,250?
Recall the distribution of weekly incomes of shift foremen in the glass industry. The weekly incomes follow the normal probability distribution, with a mean of $1,000 and a standard deviation of $100. What is the area under this normal curve between $840 and $1,200?
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
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
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 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?
The employees of Cartwright Manufacturing are awarded efficiency ratings based on such factors as monthly output, attitude, and attendance. The distribution of the ratings follows the normal probability distribution. The mean is 400, the standard deviation 50.(a) What is the area under the normal
Recall in an earlier example (here) we reported that the mean weekly income of a shift foreman in the glass industry follows a normal probability distribution with a mean of $1,000 and a standard deviation of$100. That is, μ = $1,000 and σ = $100. What is the likelihood of selecting a foreman
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.Monte’s 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.
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.
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 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?
List the major characteristics of a normal probability distribution.
Explain what is meant by this statement: “There is not just one normal probability distribution but a ‘family’ of them.”
The distribution of the annual incomes of a group of middle-management employees at Compton Plastics approximates a normal distribution with a mean of $47,200 and a standard deviation of $800.(a) About 68 percent of the incomes lie between what two amounts?(b) About 95 percent of the incomes lie
As part of its quality assurance program, the Autolite Battery Company conducts tests on battery life. For a particular D-cell alkaline battery, the mean life is 19 hours. The useful life of the battery follows a normal distribution with a standard deviation of 1.2 hours. Answer the following
Using the information in the preceding example (μ = $1,000, σ = $100), convert:(a) The weekly income of $1,225 to a z value.(b) The weekly income of $775 to a z value.
The weekly incomes of shift foremen in the glass industry follow the normal probability distribution with a mean of $1,000 and a standard deviation of $100. What is the z value for the income, let’s call it X, of a foreman who earns $1,100 per week? For a foreman who earns $900 per week?
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
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
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
America West Airlines reports the flight time from Los Angeles International Airport to Las Vegas is 1 hour and 5 minutes, or 65 minutes. Suppose the actual flying time is uniformly distributed between 60 and 70 minutes.a. Show a graph of the continuous probability distribution.b. What is the mean
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

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