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. 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 does it make sense that your answer will be the same as your answer in part (b)(ii)? explain.