Chapter 7.5, Problem 11P

Critical Thinking Suppose x has a distribution with $\mu =15\text{ and} \sigma =14.$

(a) If a random sample of size n = 49 is drawn, find ${\mu }_{\bar{x}},{\sigma }_{\bar{x}}$, and $P\left(15\le \bar{x}\le 17\right)$.

(b) If a random sample of size n = 64 is drawn, find ${\mu }_{\bar{x}},{\sigma }_{\bar{x}}$, and $P\left(15\le \bar{x}\le 17\right)$.

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? Hint: Consider the standard deviations in parts (a) and (b).