Chapter 7.5, Problem 12P

Critical Thinking Suppose an x distribution has mean µ = 5. Consider two corresponding $\bar{x}$ distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.

(a) What is the value of the mean of each of the two $\bar{x}$ distributions?

(b) For which $\bar{x}$ distribution is $P\left(\bar{x}>6\right)$ smaller? Explain.

(c) For which $\bar{x}$ distribution is $P\left(4<\bar{x}>6\right)$ greater? Explain.