Question: Three economists are arguing about the proportion of students in their Principles of Economics class who do their homework “most of the time.” They decide to settle this question by randomly selecting 15 of their 300 students and asking for proof that the students did, or did not, do their homework “most of the time.” Dr A is sure that 80% or more of his students do their homework “most of the time.” If Dr. A is correct, what is the probability that at least 13 students in the sample can show that they do their homework “most of the time”?

a) Define the random variable for this question.

Let X =

b) Explain exactly how X is distributed.

(hint: X is a ________ RV with ________ b/c …)

c) What is the probability that at least 13 students can show that they do their homework most of the time?