# Question: The shape of the distribution of the time required to

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 for an oil change is 11.4 minutes, and the standard deviation for oil-change time is 3.2 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 of less than 10 minutes?

(c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 a.m. and 12 p.m. Treating this as a random sample, what mean oil-change time would there be a 10% chance of being at or below? This will be the goal established by the manager.

(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 of less than 10 minutes?

(c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 a.m. and 12 p.m. Treating this as a random sample, what mean oil-change time would there be a 10% chance of being at or below? This will be the goal established by the manager.

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