In a large professional organization, a proportion p = 0.745 are males. We intend to take a random sample of size n from this population. Call the proportion in the sample that is male.

(a) What is the mean value for ?

(b) Compute the SD() when (i) n = 20, (ii) n = 200, and (iii) n = 2000.

Write a sentence explaining how the value for SD() changes as n increases.

(c) For which of the three values for n in Part (b) may we assume that  will have a normal distribution?

(d) Suppose n = 200. Please complete the following sentence: In this case, the sampling distribution of  is approximately the N(         ,            ) model.

(e) Call the proportion in the sample that is female. If n = 200, compute SD(). Does it make sense that your answer will be the same as your answer in Part (b)(ii)? Explain.