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 45 months and a standard deviation of 10 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 55 and 75 months?

Answer 1

Solution :

Given that ,

mean = =45

standard deviation = = 10

P(55< x < 75) = P[(55 - 45) /10 < (x - ) / < (75 - 45 ) /10 )]

= P( 1< Z < 3)

= P(Z <3)+P(Z <1 )

using empirical rule

=99.7%/2 + 68%/2

=49.85%+34%

=83.85%