Questions 13-17. Mensa is an organization open to people who score at the 98% percentile or higher on approved standardized intelligence tests. Assume that the scores for a certain approved intelligence test are Normally distributed with mean / = 175 and standard deviation o = 25. 13. (5 points) What score is required on this exam to be eligible for Mensa membership? (Numerical Response) 14. (5 points) Dr. Z decides to take a shot at Mensa membership. Assume his test score is 1.75 standard deviations above the mean. Has Dr. Z scored high enough for Mensa eligibility? Justify your answer. (Open Response) 15. (5 points) Suppose the distribution of test scores among students in this Biostat 521 class is Normally distributed with mean a = 195 and standard deviation o = 18. What is the probability that a randomly chosen Biostat 521 student will have a score that is Mensa eligible? (Numerical Response)16. (5 points) Suppose several Biostat 521 students register to take the exam. How many students would need to take the exam for you to expect at least one will achieve a Mensa eligible score? (Numerical Response) 17. (5 points) Suppose that students from the other Biostat class take this exam and their scores are Normally distributed with mean a = 191 and standard deviation o = 8. What is the probability that the mean test score ( X,) among M = 108 Biostat 521 students is greater than the mean test score ( X2) among N2 = 64 students from the other Biostat class. (This is a tough one! What do you know about X - X2?)