(1) A stadium designer has placed 1,000 seats in one section of the stadium. Assume that the weights of people who will occupy those seats are i.i.d. with a mean of 150 pounds and a SD of 8v10 pounds. Define X as the total weight of people in 1,000 seats. (a) [1pt] Let's say M = E[X] (in pounds). What is ? (b) [2pts] Using CLT, find (or define) a random variable Z as a function of X such that Z (approximately) follows the standard normal distribution. (c) [2pts] Using the result of (b), fill in the blank with a number. "With chance of (about) 95%, the total weight of people in the 1,000 seats will be in the range ( pounds." (You may use 1 - (1.645) ~ 0.05 or 1 - (1.96) ~ 0.025.)