Solution-Find the probability that sample mean x exceeds 55

Suppose a random sample of n = 15 observations is selected from a population that has normal distribution with mean 50 and standard deviation 10.

a. Give the mean and the standard deviation of the sample mean X.

b. Find the probability that sample mean X exceeds 55.

c. Find the probability that the sample mean deviates from the population mean by less than 4.

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