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 11.2 minutes, and the standard deviation is 4.6 minutes. Complete parts (a) through (c). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? A. The normal model cannot be used if the shape of the distribution is unknown. B. The sample size needs to be less than or equal to 30. C. The sample size needs to be greater than or equal to 30. D. Any sample size could be used. (b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time less than 10 minutes? The probability is approximately

Explanation / Answer

P(Xbar < 10)

mean = 11.2 , sd (X) = 4.6 , n = 35

sd(Xbar) = 4.6/sqrt(35) = 0.7775419

Z = (Xbar - 11.2)/0.7775419

P(Xbar <10)

P(Z< (10 -  11.2)/0.77754)

= P(Z< -1.5433289)

=0.0614

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