Question

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 1

P = 0,0012 or P = 0.12 %

Explanation:

We know for normal distribution that:

μ ± σ in that range we find 68.3 % of all values

μ ± 2σ ⇒ 95.5 % and

μ ± 3σ ⇒ 99.7 %

Fom problem statement

We have to find (approximately) % of cars that reamain in service between 71 and 83 months

65 + 6 = 71 ( μ + σ ) therefore 95.5 % of values are from 59 and up to 71 then by symmetry 95.5/2 = 49.75 of values will be above mean

Probability between 65 and 71 is 49.75 %

On the other hand 74 is a value for mean plus 1, 5 σ and

74 is the value limit for mean plus 1,5 σ and correspond to 49,85 (from z=0 or mean 65).

Then the pobabilty for 83 have to be bigger than 49.85 and smaller than 0,5 assume is 49.87

Finally the probability approximately for cars that remain in service between 71 and 83 months is : 0,4987 - 0.49.75

P = 0,0012 or P = 0.12 %