(Solution) - Suppose a random sample of n 25 observations is -(2025 Original AI-Free Solution)

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Suppose a random sample of n = 25 observations is selected from a population that is normally distributed with mean equal to 106 and standard deviation equal to 12.
a. Give the mean and the standard deviation of the sampling distribution of the sample mean .
b. Find the probability that exceeds 110.
c. Find the probability that the sample mean deviates from the population mean µ = 106 by no more than 4.