The shape of the distribution of the time required to get an oil change at a 20

Question

The shape of the distribution of the time required to get an oil change at a 20 -minute oil-change facility is unknown. However, records indicate that the mean time is 21.3 minutes , and the standard deviation is 4.8 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 nequals 35 oil changes results in a sample mean time less than 20 minutes? (a) Choose the required sample size below. A. Any sample size could be used. B. The normal model cannot be used if the shape of the distribution is unknown. 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.

According Central limit theorem, sampling distrbution approaches normal no matter what the original distribution as the the sample size increase. Generally a sample size greater than 30 is suggested.

b) n = 35, Z = (X - mean)/(s/sqrt(n))

P(X < 20) = P(Z < (20-21.3)/(4.8/sqrt(35))) = P(Z < -1.6023) = 0.0545

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