Section 3.2 Measures of Spread 121 39. Time to review: The following table presents the time taken to review articles that were submitted for publication to the journal Technometrics during a recent year. A few articles took longer than 9 months to review; these are omitted from the table. Consider the data to be a population. Time (Months) Number of Articles 0.0–0.9 45 1.0–1.9 17 2.0–2.9 18 3.0–3.9 19 4.0–4.9 12 5.0–5.9 14 6.0–6.9 13 7.0–7.9 22 8.0–8.9 11 a. Approximate the variance of the times. b. Approximate the standard deviation of the times. 40. Age distribution: The ages of residents of Banks City, Oregon, are given in the following frequency distribution. Consider these data to be a population. Age Frequency 0–9 283 10–19 203 20–29 217 30–39 256 40–49 176 50–59 92 60–69 21 70–79 23 80–89 12 90–99 3 Source: U.S. Census Bureau a. Approximate the variance of the ages. b. Approximate the standard deviation of the ages. 41. Drivers test: The GMAC Insurance company reported that the mean score on the 2009 National Drivers Test was 76.6 with a standard deviation of 2.7 points. The test scores are approximately bell-shaped. Estimate the percentage of participants in the test who had scores between a. 68.5 and 84.7 b. 73.9 and 79.3 c. Between what two values will approximately 95% of the scores be? 42. Pay your bills: In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 32 with a standard deviation of 7 days. Assume the data to be approximately bell-shaped. a. Between what two values will approximately 68% of the numbers of days be? b. Estimate the percentage of customer accounts for which the number of days is between 18 and 46. c. Estimate the percentage of customer accounts for which the number of days is between 11 and 53. 43. Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 621 babies born in New York. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between a. 2363 grams and 4105 grams b. 1492 grams and 4976 grams 44. Internet providers: In a survey of 600 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $64.20 with standard deviation $11.77. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between a. $40.66 and $87.74 b. $52.43 and $75.97
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