The shape of the distribution of the time requared to get an ol change at a 15-m

Question

The shape of the distribution of the time requared to get an ol change at a 15-minute oilchange facilty is unknown However, records indicate that the mean time is 16 5 minutes, and the standard deviation is 4 2utes (a) To compute probabilises regarding the sample mean using the normal model, what size sample would be required? (b) What is the probability that a random sample of n 40 ail changes sesults in a sample mean Sme less than 15 minutes? (a) Choose the required sample size below OA The normal model cannot be used dthe shape of the distrbton is unknown O B. The sample sue needs to be greater than 30 O C. Any sample size could be used O D. The sample size needs to be less than 30 b) The probablity is approxnmately Round to four decrmal places an needed )

Explanation / Answer

a) option B is correct

b)

std error of mean =std deviation/(n)1/2 =4.2/(40)1/2 =0.664

therefore probability=P(X<15)=P(Z<(15-16.5)/0.664)=P(Z<-2.2588)=0.0119

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