Statistics Chapter 6, 7 & 9 Lind, Statistical Techniques and Economics 1. Industry standards suggest that 9 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 14 Nissans yesterday. (Round your mean answer to 2 decimal places and the other answers to 4 decimal places.) a. What is the probability that none of these vehicles requires warranty service? Probability b. What is the probability exactly one of these vehicles requires warranty service? Probability c. Determine the probability that exactly two of these vehicles require warranty service. Probability_________? d. Compute the mean and standard deviation of this probability distribution. Mean Standard deviation 2. In a binomial distribution, and . Find the probabilities of the following events. (Round your answers to 4 decimal places.) a. Probability b. Probability c. Probability It is asserted that 65% of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of eight cars: a. All eight will have the transponder. (Round your answer to 4 decimal places.) 3. Probability b. At least two will have the transponder. (Round your answer to 4 decimal places.) Probability c. None will have a transponder. (Round your answer to 6 decimal places.) Probability 4. The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 6 of the 35 possible numbers. Assume there are 35 ping-pong balls each with a single number between 1 and 35. Any number appears only once, and the winning balls are selected without replacement. a. The commission reports that the probability of matching all the numbers are 1 in 1,623,160. What is this in terms of probability? (Round your answer to 8 decimal places.) Probability b. Use the hypergeometric formula to find the probability of matching all 6 winning numbers. The lottery commission also pays if a contestant matches 4 or 5 of the 6 winning numbers. Hint: Divide the 35 numbers into two groups, winning numbers and nonwinning numbers. (Round your answer to 8 decimal places.) Probability c. Find the probability, again using the hypergeometric formula, for matching 4 of the 6 winning numbers. (Round your answer to 8 decimal places.) Probability d. Find the probability of matching 5 of the 6 winning numbers. (Round your answer to 8 decimal places.) Probability 5. It is estimated that .56 percent of the callers to the Customer Service department of Dell Inc. will receive a busy signal. What is the probability that of today's 1,300 callers at least 5 received a busy signal? Use the poisson approximation to the binomial. (Round your answer to 4 decimal places.) Probability 6. In a recent survey, 45 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of eight people and ask them to name their favorite flavor of ice cream. a. How many of those in the sample would you expect to name chocolate? (Round your answer to the nearest whole number.) Expected number of people b. What is the probability exactly five of those in the sample name chocolate? (Round your answer to 4 decimal places.) Probability c. What is the probability five or more name chocolate? (Round your answer to 4 decimal places.) Probability 7. Topten is a leading source on energy-efficient products. Their list of the top six brands in terms of fuel efficiency for 2014 includes eleven Hondas. a. Determine the probability distribution for the number of Hondas in a sample of three cars chosen from the top eleven. (Round your answers to 3 decimal places.) X P(X) 0 1 2 b. What is the likelihood that in the sample of three at least one Honda is included? (Round your answer to 3 decimal places.) Probability 8. An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 2.7 non-work-related e-mails per hour. Assume the arrival of these e-mails is approximated by the Poisson distribution. a. What is the probability Linda Lahey, company president, received exactly 1 non-work-related e-mail between 4 P.M. and 5 P.M. yesterday? (Round your answer to 4 decimal places.) Probability b. What is the probability she received 8 or more non-work-related e-mails during the same period? (Round your answer to 4 decimal places.) Probability c. What is the probability she received five or less non-work-related e-mails during the period? (Round your answer to 4 decimal places.) Probability 9. A recent CBS News survey reported that 75% of adults felt the U.S. Treasury should continue making pennies. Suppose we select a sample of 10 adults. a-1. How many of the 10 would we expect to indicate that the Treasury should continue making pennies? (Round your answer to 2 decimal places.) Expected adults a-2. What is the standard deviation? (Round your answer to 4 decimal places.) Standard deviation b. What is the likelihood that exactly 7 adults would indicate the Treasury should continue making pennies? (Round your answer to 4 decimal places.) Likelihood c. What is the likelihood at least 7 adults would indicate the Treasury should continue making pennies? (Round your answer to 4 decimal places.) Likelihood 10. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $16 and $32 per share. What is the probability that the stock price will be: a. More than $27? (Round your answer to 4 decimal places.) Probability b. Less than or equal to $24? (Round your answer to 4 decimal places.) Probability 11. Dottie's 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 12% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 53 returns, what is the probability that she makes errors on: a. More than 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability b. At least 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability c. Exactly 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability 12. [The following information applies to the questions displayed below.] 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 0.40 hour (24 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.3 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends: rev: 05_18_2015_QC_CS-14973 -2-2 http://ezto.mhedu a. Less than 21 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.) Proportion Age 75 and over Ages 15 to 19 13. b. More than two hours. (Round your answers to 4 decimal places.) Proportion Age 75 and over Ages 15 to 19 14 Between 42 minutes and 126 minutes using a computer for leisure. (Round your answers to 4 decimal . . places.) Proportion Age 75 and over Ages 15 to 19 15 Find the 28th percentile. seventy two percent spend more than what amount of time? (Round your answers . d. to 2 decimal places.) Amount of time for individuals ages 75 and over Amount of time for individuals ages 15 to 19 minutes minutes 16. 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 $10.50. What is the percentage of items that cost: -2-2 http://ezto.mhedu a. Less than $7.50? (Round your answer to 4 decimal places.) Probability 17 . More than $11.50? (Round your answer to 4 decimal places.) b. Probability 18. c. Between $8.50 and $10.50? (Round your answer to 4 decimal places.) Probability 19. d. Find the 50th percentile. Fifty percent of the supermarket items cost more than what amount? (Round your answer to 2 decimal places.) Amount $ 20. 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. The members are identified by numbering them 00 through 34. We want to select a random sample of five dealers. The random numbers are: 19, 78, 28, 34, 31, 37, 45, 61, 77, 67, 11 and 45. Which dealers would be included in the sample? (Enter the numbers as they appear.) A sample is to consist of every eighth dealer. The number 0 is selected as the starting point. Which dealers are included in the sample? A population consists of the following five values: 12, 13, 19, 20, and 23. 21. a. List all samples of size 3, and compute the mean of each sample. (Round your mean value to 2 decimal places.) Sample Values 1 (Click to select) 2 (Click to select) 3 (Click to select) 4 (Click to select) 5 (Click to select) 6 (Click to select) 7 (Click to select) 8 (Click to select) 9 (Click to select) 10 (Click to select) Sum Mean b. Compute the mean of the distribution of sample means and the population mean. (Round your answers to 2 decimal places.) Sample means Population mean 22. A normal population has a mean of 60 and a standard deviation of 11. You select a random sample of 9. Compute the probability the sample mean is (Round z values to 2 decimal places and final answers to 4 decimal places): a. Greater than 63. Probability b. Less than 57. Probability c. Between 57 and 63. Probability 23. A normal population has a mean of 70 and a standard deviation of 3. You select a sample of 35. Compute the probability the sample mean is (Round z values to 2 decimal places and final answers to 4 decimal places): a. Less than 69. Probability b. Between 69 and 71. Probability c. Between 71 and 72. Probability d. Greater than 72. Probability 24. In the Department of Education at UR University, student records suggest that the population of students spends an average of 6.50 hours per week playing organized sports. The population's standard deviation is 3.50 hours per week. Based on a sample of 64 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates. a. Compute the standard error of the sample mean. (Round your answer to 2 decimal places.) Standard error b. What is the chance HLI will find a sample mean between 5.6 and 7.4 hours? (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.) Chance c. Calculate the probability that the sample mean will be between 6.1 and 6.9 hours. (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.) Probability d. How strange would it be to obtain a sample mean greater than 8.70 hours? . (Click to select) 25. Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 73, 88, 90, 95, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents. a. How many different samples, without replacement, of two test grades are possible? Different samples c. Compute the mean of the sample means and compare it to the population mean. (Round your answers to 3 decimal places.) The mean of the sample means is The population mean is (Click to select) Both means are 26. The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week. Technician Taylor Hurley Gupta Rousche Huang Shutdowns 5 4 6 4 2 a. How many samples, without replacement, of size two are possible? Different samples c. Compute the mean of the sample means and compare it to the population mean. (Round your answers to 1 decimal place.) The mean of the sample means is The population mean is Both means are (Click to select) 27. Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35 hours. hours and a standard deviation of 5.2 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries. a. What can you say about the shape of the distribution of the sample mean? Sample mean (Click to select) b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.) Standard error c. What proportion of the samples will have a mean useful life of more than 36 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability d. What proportion of the sample will have a mean useful life greater than 34 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability 28. CRA CDs Inc. wants the mean lengths of the "cuts" on a CD to be 132 seconds (2 minutes and 12 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 7 seconds. Suppose we select a sample of 18 cuts from various CDs sold by CRA CDs Inc. a. What can we say about the shape of the distribution of the sample mean? Sample mean (Click to select) b. What is the standard error of the mean? (Round your z-value to 2 decimal places and final answer to 2 decimal places.) seconds. Standard error of the mean c. What percent of the sample means will be greater than 135 seconds? (Round your z-value to 2 decimal places and final answer to 2 decimal places.) Percent % d. What percent of the sample means will be greater than 126 seconds? (Round your answer to 2 decimal places.) Percent % e. What percent of the sample means will be greater than 126 but less than 135 seconds? (Round your z-value to 2 decimal places and final answer to 2 decimal places.) % Percent e. What proportion of the sample will have a mean useful life between 34 and 36 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability 29. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $136,000. This distribution follows the normal distribution with a standard deviation of $36,000. a. If we select a random sample of 78 households, what is the standard error of the mean? (Round your answer to the nearest whole number.) Standard error of the mean b. What is the expected shape of the distribution of the sample mean? Sample mean (Click to select) c. What is the likelihood of selecting a sample with a mean of at least $141,000? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability d. What is the likelihood of selecting a sample with a mean of more than $131,000? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability e. Find the likelihood of selecting a sample with a mean of more than $131,000 but less than $141,000. (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability