A. Complete the table below and solve the expected mean, variance, and standard deviation. (15 points) Show your solution. X P(X) 2 0.21 4 0.18 6 0.13 0.31 10 0.17 X-P(X) X2 X2 P(X) B. Given a normally distributed set of scores with mean = 87.5 and standard deviation = 12.4, determine the approximate location of the following scores in terms of the standard deviation. (2 points each) Show your solution. 1. X = 66.3 2. X=80 3. X=112 4. X = 52 5. X = 63 C. Complete the table below with the appropriate values. (2 points each) Show your formula and solution. Z (1) X 20 50 17 3.21 (2) 85 13 1.89 30 (3) 1.09 0.07 108 101 (4) (5) 340 400 31 I. Find the possible values of the random variable described in each situation. (2 points each) 1. Two balls are drawn in succession without replacement from an urn containing 4 red balls and 5 blue balls. Let R be the random variables representing the number of red balls. Find the values of the random variable R. 2. In a hospital, a statistician records the sex of newborn babies. Let M be the random variable representing males among five newborn babies. 3. Let Z be a random variable representing the result of rolling a die. 4. Four coins are tossed. Let T be the random variable representing the number of tails that occur. Find the values of the random variable T 5. From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession. Each ball is placed back in the box before the next draw is made. Let G be a random variable representing the number of green balls that occur. Find the values of the random variable G.