Suppose x has a distribution with $\mu = 24$ and $\sigma = 20$.
(a) If a random sample of size $n = 46$ is drawn, find $\mu_{\bar{x}}$, $\sigma_{\bar{x}}$ and $P(24 \le \bar{x} \le 26)$. (Round $\sigma_{\bar{x}}$ to two decimal places and the
probability to four decimal places.)
$\mu_{\bar{x}} =$
$\sigma_{\bar{x}} =$
$P(24 \le \bar{x} \le 26) =$
(b) If a random sample of size $n = 73$ is drawn, find $\mu_{\bar{x}}$, $\sigma_{\bar{x}}$ and $P(24 \le \bar{x} \le 26)$. (Round $\sigma_{\bar{x}}$ to two decimal places and the
probability to four decimal places.)
$\mu_{\bar{x}} =$
$\sigma_{\bar{x}} =$
$P(24 \le \bar{x} \le 26) =$
(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).)
The standard deviation of part (b) is --Select-- part (a) because of the --Select-- sample size. Therefore, the
distribution about $\mu_{\bar{x}}$ is --Select--
