96 CHAPTER 2 Descriptive Statistics Using the Empirical Rule In Exercises 29–34, use the Empirical Rule. 29. The mean speed of a sample of vehicles along a stretch of highway is 67 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 63 miles per hour and 71 miles per hour. (Assume the data set has a bell-shaped distribution.) 30. The mean monthly utility bill for a sample of households in a city is $70, with a standard deviation of $8. Between what two values do about 95% of the data lie? (Assume the data set has a bell-shaped distribution.) 31. Use the sample statistics from Exercise 29 and assume the number of vehicles in the sample is 75. (a) Estimate the number of vehicles whose speeds are between 63 miles per hour and 71 miles per hour. (b) In a sample of 25 additional vehicles, about how many vehicles would you expect to have speeds between 63 miles per hour and 71 miles per hour? 32. Use the sample statistics from Exercise 30 and assume the number of households in the sample is 40. (a) Estimate the number of households whose monthly utility bills are between $54 and $86. (b) In a sample of 20 additional households, about how many households would you expect to have monthly utility bills between $54 and $86? 33. The speeds for eight vehicles are listed. Using the sample statistics from Exercise 29, determine which of the data entries are unusual. Are any of the data entries very unusual? Explain your reasoning. 70, 78, 62, 71, 65, 76, 82, 64 34. The monthly utility bills for eight households are listed. Using the sample statistics from Exercise 30, determine which of the data entries are unusual. Are any of the data entries very unusual? Explain your reasoning. $65, $52, $63, $83, $77, $98, $84, $70 35. Using Chebychev’s Theorem You are conducting a survey on the number of pets per household in your region. From a sample with n = 40, the mean number of pets per household is 2 pets and the standard deviation is 1 pet. Using Chebychev’s Theorem, determine at least how many of the households have 0 to 4 pets. 36. Using Chebychev’s Theorem Old Faithful is a famous geyser at Yellowstone National Park. From a sample with n = 100, the mean interval between Old Faithful’s eruptions is 101.56 minutes and the standard deviation is 42.69 minutes. Using Chebychev’s Theorem, determine at least how many of the intervals lasted between 16.18 minutes and 186.94 minutes. (Adapted from Geyser Times) 37. Using Chebychev’s Theorem The mean score on a Statistics exam is 82 points, with a standard deviation of 3 points. Apply Chebychev’s Theorem to the data using k = 4. Interpret the results. 38. Using Chebychev’s Theorem The mean number of runs per game scored by the Los Angeles Dodgers during the 2020 World Series was 5.3 runs, with a standard deviation of 1.8 runs. Apply Chebychev’s Theorem to the data using k = 2. Interpret the results. (Source: Major League Baseball)
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