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 42 months and a standard deviation of 6 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 54 and 60 months?

Answer 1

Let the number of months in service for the fleet be denoted by X which follow a bell-shaped distribution i.e. Normal distribution. It is given that,

Mean of X is 42 and the standard deviation of X is 6. Thus, we can say X~N(42,62)

We know that, by 68-95-99.7 rule,

• P(μ-σ< X <μ+σ ) =0.6826               
• P(μ-2σ< X <μ+2σ ) =0.9544
• P(μ-3σ< X <μ+3σ ) =0.9973

here, μ=42 and σ=6

we have to find that P(54<X<60)