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 50 months and a standard deviation of 5 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 60 and 65 months?

Answer 1

Soltuion:

Given that,

=  50

= 5

So,

Using empirical rule

P( - 3< X < + 3) = 99.7%

P(50 - 3* 5< X < 50 + 3* 5) = 99.7%

P(35 < X < 65 ) = 99.7%

P ( x ≤ 35) =0.0015

P ( x ≤ 40) =0.025

P ( x ≤ 45) =0.16

P ( x ≤ 55) =0.84

P ( x ≤ 60) =0.975

P ( x ≤ 65) =0.9985

P(60≤ X ≤ 65 ) )=P ( x ≤ 65)−P ( x ≤ 60)

= 0.9985 - 0.975

= 0.0235

Probability = 0.0235