## Related questions with answers

The Economic Policy Institute periodically issues reports on wages of entry level workers. The institute reported that entry level wages for male college graduates were $\$21.68$ per hour and for female college graduates were $\$18.80$ per hour in 2011 (Economic Policy Institute website, March 30, 2012). Assume the standard deviation for male graduates is $\$2.30$, and for female graduates it is $\$2.05$.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $\$.50$ of the population mean, $\$21.68$?

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $\$.50$ of the population mean, $\$18.80$?

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $\$.50$ of the population mean? Why?

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $\$.30$ below the population mean?

Solution

VerifiedGiven,

$\begin{align*} \mu_{\textrm{male}}&= 168,000 &~\sigma_{\textrm{male}}&= 40,000\\ \mu_{\textrm{female}}&= 117,000&~\sigma_{\textrm{female}}&= 25,000\\ \end{align*}$

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