The heights of pecan trees are normally distributed with a mean of 10 feet and a standard

deviation of 2 feet.

14. Show all work. Just the answer, without supporting work, will receive no credit.

(a) For a sample of 36 pecan trees, state the standard deviation of the sample mean (the “standard error of the mean”). (Round your answer to three decimal places)

(b) Suppose a sample of 36 pecan trees is taken. Find the probability that the sample mean heights is between 9.5 and 10 feet. (Round your answer to four decimal places)