The shape of the distribution of the time required to get an oil change at a 10?

Question

The shape of the distribution of the time required to get an oil change at a 10?-minute ?oil-change facility is unknown.? However, records indicate that the mean time is 11.1 minutes?, and the standard deviation is 4.4 minutes. ?(a) To compute probabilities regarding the sample mean using the normal? model, what size sample would be? required? ?(b) What is the probability that a random sample of nequals45 oil changes results in a sample mean time less than 10 ?minutes? ?(a) Choose the required sample size below. A. The normal model cannot be used if the shape of the distribution is unknown. B. Any sample size could be used. C. The sample size needs to be less than 30. D. The sample size needs to be greater than 30.

Explanation / Answer

a) D. The sample size needs to be greater than 30.

b)

P(Xbar<10)=P(Z<(10-11.1)*sqrt(45)/4.4)=P(Z<-1.68)=0.0465

c)

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