Admissions offices at universities and colleges keep careful records of acceptance and yield rates. The yield rate is the percentage of admitted students who decide to accept an offer of admission....

Admissions offices at universities and colleges keep careful records of acceptance and yield rates. The yield rate is the percentage of admitted students who decide to accept an offer of admission. Historical data help them to plan for the incoming classes and guide some admission decisions. The yield rate for Yale University is 64.1%.23 Suppose 100 students who were accepted to Yale are randomly selected.

a. Find the probability that the sample proportion of those who enroll is less than 0.55.

 b. Find the probability that the sample proportion of those who enroll is between 0.60 and 0.65.

c. Suppose the actual sample proportion of those who enroll is 0.70. Is there any evidence to suggest that the yield has increased? Justify your answer.

A certain philanthropic organization funds one out of every ten grant proposals. Suppose a random sample of 300 grant proposals is obtained.

 a. Find the probability that the sample proportion of funded grant proposals is less than 0.075.

b. Find the probability that the sample proportion of funded grant proposals is between 0.11 and 0.15.

c. If the funding rate increases, the board of directors may become concerned about resources being depleted. Suppose the actual sample proportion of funded grant proposals is 0.16. Is there any evidence to suggest that the funding rate has increased? Justify your answer.