According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical, civil, and industrial) were women. Suppose a random sample of 50 engineers is selected.

a. How likely is it that the random sample of 50 engineers will contain 8 or more women in these positions?

b. How likely is it that the random sample will contain fewer than 5 women in these positions?

c. If the random sample included 200 engineers, how would this change your answer to part b?