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Question 6: (10pts) Suppose that in a particular application requiring a single battery, the mean lifetime of the battery is 4 weeks, with a standard deviation of 1 week. The battery is replaced by a new one when it dies, and so on. Assume the lifetime of each battery is independent. What, approximately, is the probability that more than 24 replacements will have to be made in a two-year period, starting at the time of installation of a new battery? [Hint: Normal approximation. For each year we assume that there are 52 weeks. Assume X is the lifetime in weeks of the i-th battery, and S= X7+X}+X,+ +X,, is approximately normally distributed. As such, the question turns out to be finding the probability that S