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 ​21.2 minutes, and the standard deviation is 3.9 minutes. What is the probability that a random sample of n oil changes results in a sample mean time less than 20 ​minutes?

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 45 oil changes between 10 A. M. and 12 P. M. Treating this as a random​ sample, there would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.

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