1. 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?

2. TransUnion is a leading global provider of business intelligence services. Transunion reported that 33% of the mortgages in the year previous to the sub-prime mortgage crisis were adjustable-rate mortgages (ARMs).

a. In samples of mortgages of size 75, what proportion of the samples would you expect to produce sample proportions equal to or larger than 0.25?

b. If a sample of size 75 produced a sample proportion of 0.45, what would you infer that the population proportion of mortgages with ARMs really is?

c. In a sample of 90 mortgages, what would the probability be that the number of mortgages with ARMS would be between 25 and 35?