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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 58 months and a standard deviation of 3 months. using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 61 and 64 months?



Answer :

Approximately 99.7% ( or 99.73% ) population  lies within  3 standard deviation   ( μ - 3σ , μ + 3σ ) = ( 38, 68 ) .

Why is there a standard deviation?

  • The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
  • Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.              

Empirical rule holds only for normal populations and states that

approximately 68% ( or 68.27%) population lies within  standard deviation

                          ( μ - σ , μ + σ ) = ( 48 , 58 )

Approximately 95% ( or 95.45% ) population  lies within 2  standard deviation  

                    ( μ - 2σ , μ + 2σ ) = ( 43, 63 )

Approximately 99.7% ( or 99.73% ) population  lies within  3 standard deviation  

                        ( μ - 3σ , μ + 3σ ) = ( 38, 68 )

Learn more about standard deviation  

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