Researchers are studying two populations of sea turtles. In population D. 30 percent of the turtles have a shell length greater than 2 feet. In
population E, 20 percent of the turtles have a shell length greater than 2 feet. From a random sample of 40 turtles selected from D, 15 had a
shell length greater than 2 feet. From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet. Let PD
represent the sample proportion for D, and let PE represent the sample proportion for E.

(a) What is the value of the difference PD - PE? Show your work

(b) What are the mean and standard deviation of the sampling distribution of the difference in sample proportions PD - PE? Show your work and label each value.

(c) Can it be assumed that the sampling distribution of the difference of the sample proportions PD - PE is it approximately normal? Justify your answer.

(d) Consider your answer in part (a). What is the probability that PD - PE is greater than the value found in part (a)? Show your work.