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. if the random sample of 50 engineers contained 8 women, what is the sample proportion of women? provide the correct notation, and value.

b. how likely is it that the random sample of 50 engineers will contain 8 or more women in these positions? (give the proper probability statements/notation, show work, and give value to 4 decimal places)

c. how likely is it that the random sample will contain fewer than 5 women in these positions? (give the proper probability statements/notation, show work, and give value to 4 decimal places)

d. if the random sample included 200 engineers, how would this change your answer to part b? be as specific as possible.