Review Exercises 143 c. Other things being equal, is it better for a measurement method to have a smaller standard deviation or a larger standard deviation? Or doesn’t it matter? Explain. 8. Time in surgery: Records at a hospital show that a certain surgical procedure takes an average of 162.8 minutes with a standard deviation of 4.9 minutes. If the data are approximately bell-shaped, between what two values will about 95% of the data fall? 9. Rivets: A machine makes rivets that are used in the manufacture of airplanes. To be acceptable, the length of a rivet must be between 0.9 centimeter and 1.1 centimeters. The mean length of a rivet is 1.0 centimeter, with a standard deviation of 0.05 centimeter. What is the maximum possible percentage of rivets that are unacceptable? 10. How long can you talk? A manufacturer of cell phone batteries determines that the average length of talk time for one of its batteries is 470 minutes. Suppose that the standard deviation is known to be 32 minutes and that the data are approximately bell-shaped. Estimate the percentage of batteries that have z-scores between −1 and 1. 11. Paying rent: The monthly rents for apartments in a certain town have a mean of $800 with a standard deviation of $150. What can you determine about these data by using Chebyshev’s Inequality with K = 3? 12. Advertising costs: The amounts spent (in billions) on media advertising in the United States for a sample of categories in 2008 are presented in the following table. Advertising Category Amount Spent on Advertising Automotive 12.8 Financial services 9.6 Local services 8.6 Telecom 8.4 Miscellaneous retail 8.3 Direct response 7.3 Food & candy 6.0 Personal care products 6.0 Restaurants 5.6 Travel & tourism 5.2 Source: TNS Media Intelligence a. Find the mean amount spent on advertising. b. Find the median amount spent on advertising. c. Find the sample variance of the advertising amounts. d. Find the sample standard deviation of the advertising amounts. e. Find the first quartile of the advertising amounts. f. Find the third quartile of the advertising amounts. g. Find the 40th percentile of the advertising amounts. h. Find the 65th percentile of the advertising amounts. 13. Matching: Match each histogram to the boxplot that represents the same data set. a. 0 1 2 3 4 5 6 7 8 9 10 25 20 15 10 5 0 Frequency b. 0 1 2 3 4 5 6 7 8 9 10 150 120 90 60 30 0 Frequency (1) 0 1 2 3 4 5 6 7 8 9 10 (2) 0 1 2 3 4 5 6 7 8 9 10 c. 0 1 2 3 4 5 6 7 8 9 10 60 50 40 30 20 10 0 Frequency d. 0 1 2 3 4 5 6 7 8 9 10 40 30 20 10 0 Frequency (3) 0 1 2 3 4 5 6 7 8 9 10 (4) 0 1 2 3 4 5 6 7 8 9 10
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