The organizers of a mentoring program are curious about whether there

are differences in outcomes when the gender of the mentor matches the

young adult mentee. They take separate random samples of $80$ young

adults with either the same$-$gender or different$-$gender mentors to see the

difference between the sample proportions $($ hat$(p{)}_S-$hat$(p{)}_D).$ Suppose that $90\%$

of young adults with same$-$gender mentors get jobs while $84\%$ different$-$

gender mentors get jobs.

What will be the shape of the sampling distribution of hat$(p{)}_S-$hat$(p{)}_D,$ and why?

Choose $1$ answer:

Approximately normal, because we expect $72$ with jobs from those

with same$-$gender mentors, and $67\mathrm{.}2$ from those with different$-$

gender mentors, and both of these counts are at least $10.$

Approximately normal, because we expect $90$ with jobs and $10$

without jobs from those with same$-$gender mentors, and $84$ and

$16$ from those with different$-$gender mentors, and all of these

counts are at least $10.$

Not normal, because we expect fewer than $10$ young adults

without jobs with same$-$gender mentors.

Not normal, because we expect fewer than $10$ young adults

without jobs with different$-$gender mentors.