An emergency room administrator wants to know the proportion of emergency room patients who spend more than one hour before being attended to. He knows that the time of arrival at the emergency room and the time of seeing the first medical staff member are both recorded. He draws a random sample of 50 records and discovers 14 indicating that the person spent more than one hour waiting.

a. what is the probability that the true proportion of persons spending more than one hour is 36 percent or more?

b. What is the probability that the true proportion of persons spending more than one hour is 20 percent or less?

c. What is the probability that the true proportion of persons spending more than one hour is from 24 to 32 percent?