18. Suppose the random variable x is best described by a normal distribution with V = 30 - 7,9. Find the z-score that corresponds to each of the following x values. and o = x=36, z x=35, z b. X=22, z x=30, z d. x=19, z e. x=36, z 19. Assume that the readings on the thermometers are normally idistributed with a mean of 00 and a standard deviation of 1.000C. Find P25i the 25th percentile. This is the temperature reading separating the bottom 25 % from the top 75 0/0, 20. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Mensa is an international society that has one and only one qualification for membership: a score in the top 2% on an IQ test. a. What IQ score should one have in order to be eligible for Mensa? b. In a typical region of 115,000 people, how many are eligible for Mensa? 21. Find the following probabilities for the standard normal random variable z a. P(-1.36szs b. P(-2.27 c. .P(zs = 10.1 and o = 3.4. Find each 22. Suppose x is a normally distributed random variable with of the following probabilities: a. P(5.7 16.2): b. P(5.6 15.6)- d. P(X2 10.7)- e. P(XS 23. Women's weights are normally distributed with a mean given by = 143 lb and a standard deviation given by o = 29 lb. Find the third decile, D3, which separates the bottom 30% from the top 700/0.