Problem 4 The Central Limit Theorem states: Let X1, ..., Xn be a random sample with E[X;] = µ and Var(X¡) = o?. If n is sufficiently large, then X has approximately a normal distribution with mean ui...

Extracted text: Problem 4 The Central Limit Theorem states: Let X1, ..., Xn be a random sample with E[X;] = µ and Var(X¡) = o?. If n is sufficiently large, then X has approximately a normal distribution with mean ui = µ and variance o? = o?In. It's also true that E X, ~ N(nu, no²). Suppose a machine requires a specific type of battery that lasts an exponential amount of time with mean 25 hours. As soon as the battery fails, you replace it immediately. If you have 50 such batteries, estimate the probability that the machine is still operating after 1300 hours. Round your answer to three decimal places. Save your answer as p4.