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theory of statistics

Questions and Answers of Theory of Statistics

A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few
A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 12 hours, with a standard deviation of
The estimate of the population proportion is to be within plus or minus .10, with a 99 percent level of confidence. The best estimate of the population proportion is .45. How large a sample is
We want to estimate the population mean within 5, with a 99 percent level of confidence.The population standard deviation is estimated to be 15. How large a sample is required?
A population is estimated to have a standard deviation of 10. We want to estimate the population mean within 2, with a 95 percent level of confidence. How large a sample is required?
There are 300 welders employed at the Maine Shipyards Corporation. A sample of 30 welders revealed that 18 graduated from a registered welding course. Construct the 95 percent confidence interval for
The attendance at the Savannah Colts minor league baseball game last night was 400. A random sample of 50 of those in attendance revealed that the mean number of soft drinks consumed per person was
Thirty-six items are randomly selected from a population of 300 items. The sample mean is 35 and the sample standard deviation 5. Develop a 95 percent confidence interval for the population mean.
Schadek Silkscreen Printing, Inc. purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a
Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters
The owner of the West End Kwick Fill Gas Station wished to determine the proportion of customers who use a credit card or debit card to pay at the pump. He surveys 100 customers and finds that 80
The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following
Merrill Lynch Securities and Health Care Retirement, Inc., are two large employers in downtown Toledo, Ohio. They are considering jointly offering child care for their employees. As a part of the
The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20
The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an avera:ge of 20 eggs per month with a standard deviation of 2
Use Appendix F to locate the value of t under the following conditions.a. The sample size is 15 and the level of confidence is 95 percent.b. The sample size is 24 and the level of confidence is 98
Use Appendix F to locate the value of t under the following conditions.a. The sample size is 12 and the level of confidence is 95 percent.b. The sample size is 20 and the level of confidence is 90
Dr. Patton is a Professor of English. Recently he counted the number of misspelled words in a group of student essays. For his class of 40 students, the mean number of misspelled words was 6.05 and
Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. From his records, he selects a random sample of 60 sales and
Refer to the previous exercise. Suppose that 64 smokers (instead of 49) were sampled. Assume the sample mean and the sample standard deviation remained the same ($20 and $5, respectively).a. What is
A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 49 steady smokers revealed that X = $20 and s = $5.a. What is the point
Suppose you want an 85 percent confidence level. What value would you use to multiply the standard error of the mean?
A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 5. The sample mean is 20.a. Determine the standard error of the mean.b.
A sample of 81 observations is taken from a normal population. The sample mean is 40, and the sample standard deviation is 5. Determine the 95 percent confidence interval for the population mean.
A sample of 49 observations is taken from a normal population. The sample mean is 55, and the sample standard deviation is 10. Determine the 99 percent confidence interval for the population mean.
Refer to the CIA data, which reports demographic and economic information on 46 countries. Select a random sample of 10 countries. For this sample calculate the mean GDP/capita. Repeat this sampling
Refer to the Real Estate data, which reports information on the homes sold in the Denver, Colorado, area last year.a. Compute the mean and the standard deviation of the distribution of the selling
There are several websites that will report the 30 stocks that make up the Dow Jones Industrial Average (DJIA). One site is www.dbc.com/dbcfiles/dowt.html. Compute the mean of the 30 stocks.a. Use a
You need to find the "typical" or mean annual dividend per share for large banks. You decide to sample six banks listed on the New York Stock Exchange. These banks and their trading symbol follow:a.
The following table lists the most recent data available on per capita personal income (in dollars) for each of the 50 states.
Suppose we roll a fair die two times.a. How many different samples are there?b. List each of the possible samples and compute the mean.c. On a chart similar to Chart 8-1, compare the distribution of
The mean SAT score for Division I student-athletes is 947 with a standard deviation of 205.If you select a random sample of 60 of these students, what is the probability the mean is below 900?
The mean amount purchased by each customer at Churchill's Grocery Store is $23.50. The population is positively skewed and the standard deviation is not known. For a sample of 50 customers, answer
The Crossett Trucking Company claims that the mean weight of their delivery trucks when they are fully loaded is 6,000 pounds and the standard deviation is 150 pounds. Assume that the population
A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to the Los Angeles International Airport is$18.00 and the standard
The mean age at which men in the United States marry for the first time is 24.8 years. The shape and the standard deviation of the population are both unknown. For a random sample of 60 men, what is
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution is positively skewed. The standard
Recent studies indicate that the typical 50-year-old woman spends $350 per year for personal-care products. The distribution of the amounts spent is positively skewed. We select a random sample of 40
CRA CDs, Inc. wants the mean lengths of the "cuts" on a CD to be 135 seconds (2 minutes and 15 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 1 O-minute
The Sony Corporation produces a Walkman that requires two AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the
The Appliance Center has six sales representatives at their North Jacksonville outlet. Listed below is the number of refrigerators sold by each last month.Sales Number Representative Sold Zina Craft
At the downtown office of First National Bank there are five tellers. Last week the tellers made the following number of errors each: 2, 3, 5, 3, and 5.a. How many different samples of 2 tellers are
Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the
As a part of their customer-service program, United Airlines randomly selected 10 passengers from today's 9 A.M. Chicago-Tampa flight. Each sampled passenger is to be interviewed in depth regarding
A study of motel facilities in Rock Hill, South Carolina, showed there were 25 facilities. The city's convention and visitors bureau is studying the number of rooms at each location. The results are
The manufacturer of eMachines, an economy-priced computer, recently completed the design for a new laptop model. eMachine's top management wO!-lld like some assistance in pricing the new laptop. Two
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
According to an IRS study, it takes an average of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. A consumer watchdog agency selects a random sample of 40
The mean rent for a one-bedroom apartment in Southern California is $2,200 per month.The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed.
A population of unknown shape has a mean of 75. You select a sample of 40. The standard deviation of the sample is 5. Compute the probability the sample mean is:a. Less than 74.b. Between 74 and
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
The Scrapper Elevator Company has 20 sales representatives who sell their product throughout the United States and Canada. The number of units sold by each representative is listed below. Assume
Appendix E 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? Is this
There are five sales associates at Mid-Motors Ford. The five representatives and the number of cars they sold last week are:Sales Representative Peter Hanklsh Connie Stailter Juan Lopez Ted Barnes
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 population consists of the f~lIowing 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
Listed on the next page are the 27 Nationwide Insurance agents in the Toledo, Ohio, metropolitan area. We would like to estimate the mean number of years agents are employed with Nationwide.a. We
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
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
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
Refer to the CIA data, which report demographic and economic information on 46 countries.a. The mean of the GOP/capita variable is 16.58 with a standard deviation of 9.27. Use the normal distribution
Refer to the Baseball 2003 dataset, which reports information on the 30 Major League Baseball teams for the 2003 season.a. The mean attendance per team for the season was 2,254 (in OOOs) with a
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,
In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to
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
The Cincinnati Enquirer, as part of the 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
The weights of canned hams processed at the 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
The funds dispensed at the ATM machine located near the checkout line at the Kroger's in Union, Kentucky, follows a normal distribution with a mean of $4,200 per day and a standard deviation of $720
The current model Boeing 737 has a capacity of 189 passengers. Suppose Delta Airlines uses this equipment for its Atlanta to Houston flights. The distribution of the number of seats sold for the
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
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
The annual commissions earned by sales representatives of Machine Products, Inc. a manufacturer of light machinery, follow the normal distribution. The mean yearly amount earned is $40,000 and the
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 distribution, with a
A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group, Inc., in Somers, New York,showed the calls follow the normal distribution. The mean length of time
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
The times 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
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
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
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
Assume "that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean $2,100 per hour and a standard deviation of $250. What is the operating cost for the
Refer to Exercise 20, where the amount requested for home loans followed the normal distribution with a mean of $70,000 and a standard deviation of $20,000.a. How much is requested on the largest 3
The amounts dispensed by a cola machine follow the normal distribution with a mean of 7 ounces and a standard deviation of 0.10 ounces per cOp. How much cola is dispensed in the largest 1 percent of
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.
The mean starting salary for college graduates in the spring of 2005 was $36,280. Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of
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 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
A cola-dispensing machine is set to dispense on average 7.00 ounces of cola per cup. The standard deviation is 0.10 ounces. The distribution amounts dispensed follows a normal distribution.a. What is
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
The mean of a normal probability distribution is 60; the standard deviation is 5.a. About wh:;1t percent of the observations lie between 55 and 65?b. About what percent of the observations lie
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
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
Refer to the Real Estate data,vvJli
A recent CBS News survey reported that 67 percent of adults felt the U.S. Treasury should continue making pennies.
On September 18, 2003, hurricane Isabel struck the North Carolina Coast causing extensive damage. For several days prior to reaching land the National Hurricane Center had been predicting the
According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an arti-
The National Aeronautics and Space Administration (NASA) has experienced two disasters.The Challenger exploded over the Atlantic Ocean in 1986 and the Columbia exploded over East Texas in 2003. There
New Process, Inc., a large mail-order supplier of women's fashions, advertises same-day service on every order. Recently the movement of orders has not gone as planned, and there were a large number
An internal study at Lahey Electronics, a large software development company, revealed the mean time for an internal e-mail message to arrive at its destination was 2 seconds. Further, the

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