2175-6362-US1 9. Let random variable x represent the number of heads when a fair coin is tossed three times. (a) Construct a table describing the probability distribution. (b) Determine the mean and standard deviation of x. (Round answer to two decimal places) ____________________________________________________________________________ 10. Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. (a) Let X be the number of the serves that Mimi returns. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? (b) Find the probability that that she returns at least 1 of the 8 serves from her opponent. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit. ____________________________________________________________________________ 11. The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet. 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 7 and 11 feet tall? (round the answer to 4 decimal places) (b) Find the 40th percentile of the pecan tree height distribution. (round the answer to 2 decimal places) _____________________________________________________________________________ 12. Based on the performance of all individuals who tested between July 1, 2012 and June 30, 2015, the GRE Quantitative Reasoning scores are normally distributed with a mean of 152.47 and a standard deviation of 8.93. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). Show all work. Just the answer, without supporting work, will receive no credit. (a) Consider all random samples of 49 test scores. What is the standard deviation of the sample means? (Round your answer to three decimal places) (b) What is the probability that 49 randomly selected test scores will have a mean test score that is greater than 150? (Round your answer to four decimal places) _____________________________________________________________________________ 5