2. Roll 3 die and record the sum. If the die are fair, the mean of the sum is 10.5 and the standard deviation is 2.958. To check if the die are fair, we roll the three dice 25 time recording the sum, Z1, Z2, . .. , Z25 and taking the average Z of these 25 outcomes. (a) What is the mean and the standard deviation of Z? (b) Use the central limit theorem to estimate P{Z > 10}. (c) If we repeat the experiment, rolling the three dice 50 times, does P{Z > 10} increase, decrease, or stay the same? Explain your