Question

The times required to service customers' cars at a repair shop are skewed to the right with a mean of 2.5 hours and a standard deviation of 0.75 hours. What can be said about the proportion of cars whose service time is either less than one hour or more than four hours?

at most (BLANK) % of the cars take less than one hour or more than four hours to service

Please calculate the (BLANK).

Answer 1

here for K score =(X-mean)/std deviation

therefore corresponding k score for service time of 1 hour =(1-2.5)/0.75 =-2

and corresponding k score for service time of 4 hour =(4-2.5)/0.75 =2

hence from Chebychev proportion of cars whose service time is either less than one hour or more than four hours   =P(K<-2)+P(X>2)=1/k² =1/2² =0.25

at most 25% of the cars take less than one hour or more than four hours to service