SOLUTION: 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 11.6 minutes,

Question 1076749: 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 11.6 minutes, and the standard deviation is 3.8 minutes.
 What is the probability that a random sample of n=35 oil changes results in a sample mean time less than 10 minutes?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Presumably, the sample size's being >35 is a way of saying the mean and sd of the sampling distribution follow a normal distribution due to the Central Limit Theorem.
z=(x-mean)/sigma/n, since the sd appears to be known in the population.
=(10-11.6)/3.8/sqrt (35)=-1.6*sqrt(35)/3.8=-2.49
probability z < -2.49 is 0.0064
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