Use for questions 13 and 14. The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet. 13. 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 feet tall? (Round the answer to 4 decimal places) (b) Find the 75th percentile of the pecan tree height distribution. (Round the answer to 2 decimal places) 14. Show all work. Just the answer, without supporting work, will receive no credit. (a) 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) (b) 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) 15. A survey showed that 720 of the 1000 adult respondents believe in global warming. (a) Construct a 90% confidence interval estimate of the proportion of adults believing in global warming. (Round the lower bound and upper bound of the confidence interval to three decimal places) Include description of how confidence interval was constructed. (b) Describe the results of the survey in everyday language.