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 21.8 minutes, and the standard deviation is 4.4 minutes. Complete parts (a) through (c) below (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? 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 greater than 30. D. The sample size needs to be less than 30. (b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time less than 20 minutes? The probability is approximately ___.

Explanation / Answer

A)

Sample size > 30

B)

P(X<20) P(Z<(20-21.8)/(4.4/SQRT(35))) =NORMSDIST((20-21.8)/(4.4/SQRT(35))) 0.0078

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