MGSC 239: Spring -01 Homework 5: Chapter 7 1. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $21 and $33 per share. What is the probability that the stock price will be: a. More than $30? (Round your answer to 4 decimal places.) Probability b. Less than or equal to $28? (Round your answer to 4 decimal places.) Probability 2. Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds and 12 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? (Do not round your intermediate calculations. Round your answers to 1 decimal place.) a b b-1. What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Mean b-2. What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Standard deviation c. What percent of the problems take more than 5 minutes to resolve? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) d. Suppose we wish to find the middle 50% of the problem-solving times. What are the end points of these two times? (Do not round your intermediate calculations. Round your answers to 3 decimal places.) End point 1 End point 2 3. The mean of a normal probability distribution is 440; the standard deviation is 12. a. About 68% of the observations lie between what two values? Value 1 Value 2 b. About 95% of the observations lie between what two values? Value 1 Value 2 c. Practically all of the observations lie between what two values? Value 1 Value 2 4. A normal population has a mean of 21 and a standard deviation of 5. a. Compute the z value associated with 24. (Round your answer to 2 decimal places.) Z b. What proportion of the population is between 21 and 24? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion c. What proportion of the population is less than 18? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion 5. The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 21 million with a standard deviation of 10 million. What is the probability next week's show will: a. Have between 22 and 31 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability b. Have at least 12 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability c. Exceed 37 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability 6. 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 in New York City, where the mean time is 38.5 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.2 minutes. a. What percent of the New York City commutes are for less than 26 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) b. What percent are between 26 and 34 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) c. What percent are between 26 and 45 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) 7. For the most recent year available, the mean annual cost to attend a private university in the United States was $20,082. 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? (Round z value to 2 decimal places and your final answer to the nearest whole number.) Amount $ 8. The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,400. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 620 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 95 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.) Pages 9. 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 13% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 51 returns, what is the probability that she makes errors on: a. More than 7 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability b. At least 7 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability c. Exactly 7 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability [The following information applies to the questions displayed below.] Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a mean of 50 seconds. Calculate the probability a customer waits: 10. a. Less than 30 seconds. (Round your answer to 4 decimal places.) Probability 11. b. More than 115 seconds. (Round your answer to 4 decimal places.) Probability 12 c. Between 40 and 70 seconds. (Round your answer to 4 decimal places.) Probability 13. d. Fifty percent of the patrons wait less than how many seconds? What is the median? (Round your answer to 2 decimal places.) Median _______ seconds [The following information applies to the questions displayed below.] 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 $6.50. What is the percentage of items that cost: 14. Required information a. Less than $3.50? (Round your answer to 4 decimal places.) Probability 15. Required information b. More than $7.50? (Round your answer to 4 decimal places.) Probability 16. Required information c. Between $4.50 and $6.50? (Round your answer to 4 decimal places.) Probability 17. Required information d. Find the 30th percentile. Seventy percent of the supermarket items cost more than what amount? (Round your answer to 2 decimal places.) Amount $ ReferenceseBook & Resources WorksheetDifficulty: 2 IntermediateLearning Objective: 07-05 Describe the exponential probability distribution and use it to calculate probabilities. Check my work 18.value: 5.00 points A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 5.30 minutes and the standard deviation was 0.60 minutes. a. What fraction of the calls last between 5.30 and 6.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Fraction of calls b. What fraction of the calls last more than 6.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Fraction of calls c. What fraction of the calls last between 6.00 and 7.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Fraction of calls d. What fraction of the calls last between 5.00 and 7.00 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Fraction of calls e. As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 5 percent of the calls. What is this time? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.) Duration 19.value: 5.00 points According to the South Dakota Department of Health, the number of hours of TV viewing per week is higher among adult women than adult men. A recent study showed women spent an average of 29 hours per week watching TV, and men, 24 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 4.9 hours and is 5.4 hours for the men. a. What percent of the women watch TV less than 35 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability b. What percent of the men watch TV more than 20 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability c. How many hours of TV do the four percent of women who watch the most TV per week watch? Find the comparable value for the men. (Round your answers to 3 decimal places.) Number of hours Women Men 20. 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. (Round z-score computation to 2 decimal places and your final answers to 2 decimal places.) 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