Question: For each of the following, if the scenario fits the conditions for the approximate normality of the sampling distribution for a sample proportion, describe the sampling distribution of p^{^} and draw a picture of it. If the scenario doesn't fit, explain why not (in which case you do not have the tools to describe the sampling distribution of p^{^}).

a. An auto insurance company has 1500 customers in a city, and over the long run, 6% of them will file a claim in any given year. Define p^{^} to be the proportion who file a claim in the next year.

b. A dean has found that over the years, about 15% of students who begin their college work in her program do not finish. This year, 90 students will begin her program; define p^{^} to be the proportion who will finish.

c. An essay contest has three winners, but the number of entrants varies each time that it is offered, so the proportion of entrants who are winners also varies. Define p^{^} to be the proportion of entrants who will be winners the next time that the contest is offered.