The shape of the distribution

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 3.5 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 less than 10 minutes?

Answer 1

 

 Perhaps you may have heard the rule of thumb that says something like

  the sample size must be at least 30 in order for the distribution to resemble the Normal.

 

  Anyways...

 

    the z-score is (sample mean - population mean)/ ( std dev/ sqrt(n)) =

   

                          (10-11.2)/(3.5/sqrt(40)) = -2.16

 

             Per the table the probability is 0.0154 = 1.54%