The shape of the distribution of the time required to get an oil change at a 15-

Question

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.6 minutes, and the standard deviation is 4.5 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 n = 40 oil changes results in a sample mean time less than 15 minutes? (a) Choose the required sample size below. A. The normal model cannot be used if the shape of the distribution is unknown. B. The sample size needs to be less than 30. C. The sample size needs to be greater than 30 D. Any sample size could be used.

Explanation / Answer

a)

to apply normal distribution to unkonwn distribution, the sample size should be greater than 30

b)

P(X<15) = P(Z < 15-16.6/4.5/sqrt(40))

= P(Z < -2.2487)

= 0.0123

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