Sampling behavior of a mean. Suppose you could take all possible samples of size n = 25 from a Normal population with mean μ = 50 and σ = 5.

(a) Sketch or describe in words the sampling distribution of .
Identify landmarks on the horizontal axis of this sampling distribution that are ±1 and ±2 standard deviations around its center.

(b) Would you be surprised to find a sample mean of 47 under these conditions? Explain your reasoning.

(c) Would you be surprised to find a sample mean of 51.5? Explain your reasoning.