4) Let X be the mean of a random sample, (X1, ..., X50), of size 50 drawn from a normally distributed population, with mean 112 and standard deviation 40. (a) Find the mean and standard deviation of...

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Extracted text: 4) Let X be the mean of a random sample, (X1, ..., X50), of size 50 drawn from a normally distributed population, with mean 112 and standard deviation 40. (a) Find the mean and standard deviation of X. (b) Find the probability that X assumes a value between 110 and 114. (c) Find P(X > 113). Find P(X, > 113).