The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.

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

(a) What is the probability that a randomly selected pecan tree is between 9 and 12 feettall? (Round the answer to 4 decimal places)

(b) Find the 75th percentile of the pecan tree height distribution. (Round the answer to 2decimal places)

(c) For a sample of 64 pecan trees, state the standard deviation of the sample mean (the"standard error of the mean"). (Round your answer to three decimal places)

(d) Suppose a sample of 64 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)