Jerry takes a large keg of a certain drink to a picnic. The keg is used to fill 16 ounce cups, but actually fills each cup with a random amount of drink with a mean of 16.01 ounces and a standard deviation of 0.11 ounces. Let us assume that the amount of drink, X, dispensed into any cup is independent of the amount of drink dispensed into any other cup. Suppose 101 cups of drink are dispensed at the picnic. Let M be the random variable representing the mean amount of drink per cup actually dispensed in the 101 cups. Let T = the random variable representing the total amount of drink actually dispensed in the 101 cups. a) What theorem will let us treat T and M as approximately normal random variables? O Chebychev's Theorem O Law of Large Numbers O Monte Carlo Theorem O 301 Theorem O Convolution Theorem O Central Limit Theorem b) What is the expected value of T? c) What is the standard deviation of T? d) How many ounces of drink should be put into the large keg to be 95% sure that the keg can actually dispense 101 cups of drink without running out?

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