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 21.6 minutes, and the standard deviation is 3.8 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 n=35 oil changes results in a sample mean time less than 20minutes.

(b) The probability is approximately____

(Round to four decimal places as needed.)

Explanation / Answer

a) Sample size should be greater than 30, to use normal model for computing probabilities regarding sample mean.

b) Probability that sample mean time less than 20 minutes = P( Xbar <20)

= P [Z < ( (20-21.6) / (3.8/sqrt(35)) ]

= P(Z< -2.49)

= 0.0064

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