SECTION 4.1 Probability Distributions 199 Finding the Mean, Variance, and Standard Deviation In Exercises 29–34, (a) find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results. 29. Dogs The number of dogs per household in a neighborhood Dogs 0 1 2 3 4 5 Probability 0.686 0.195 0.077 0.022 0.013 0.007 30. Baseball The number of games played in each World Series from 1903 through 2020 (Source: Major League Baseball) Games played 4 5 6 7 8 Probability 0.164 0.241 0.216 0.345 0.034 31. Machine Parts The number of defects per 1000 machine parts inspected Defects 0 1 2 3 4 5 Probability 0.263 0.285 0.243 0.154 0.041 0.014 32. Extracurricular Activities The number of school-related extracurricular activities per student Activities 0 1 2 3 4 5 6 7 Probability 0.059 0.122 0.163 0.178 0.213 0.128 0.084 0.053 33. Hurricanes The histogram shows the distribution of hurricanes that have hit the U.S. mainland from 1851 through 2019 by Saffir-Simpson category, where 1 is the weakest level and 5 is the strongest level. (Source: National Oceanic & Atmospheric Administration) Probability Category 0.05 1 2 3 4 5 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.280 0.409 0.014 0.216 U.S. Mainland Hurricanes x P(x) 0.081 Probability Rating 0.10 1 2 3 4 5 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.005 0.009 0.925 0.007 Reviewer Ratings x P(x) 0.055 FIGURE FOR EXERCISE 33 FIGURE FOR EXERCISE 34 34. Reviewer Ratings The histogram shows the reviewer ratings on a scale from 1 (lowest) to 5 (highest) of the Sony PlayStation 5. (Source: Best Buy) 35. Writing The expected value of an accountant’s profit-and-loss analysis is 0. Explain what this means. 36. Writing In a game of chance, what is the relationship between a “fair bet” and its expected value? Explain.
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