A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 65 months and a standard deviation of 6 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 71 and 83 months?

Answer:15.85%Step-by-step explanation:Empirical rule states that for a normal distribution, 68% of the data falls within one standard deviation, 95% falls within two standard deviation and 99.7% falls within three standard deviation.Given mean (μ) = 41 months, standard deviation (σ) = 5 monthsOne standard deviation = μ ± σ = 41 ± 5 = (36, 46)Therefore 68% falls within 36 months and 41 monthsTwo standard deviation = μ ± 2σ = 41 ± 2(5) = (31,51)Therefore 95% falls within 31 months and 51 monthsThree standard deviation = μ ± 3σ = 41 ± 3(5) = (26, 56)Therefore 99.7% falls within 26 months and 56 monthsThe percentage of cars that remain in service between 46 and 51 months = 32%/2 - 0.3%/2 = 16% - 0.15% = 15.85%