Question: It has been estimated that 17.0% if mutual fund shareholders are retired persons. Assuming the population proportion to be π = 0.17, and that a simple random sample of 400 shareholders has been selected:

a) what is the expected value of p = the proportion of those in the sample who are retired?

b) what is the standard error of the sampling distribution of the proportion, p?

c) what is the probability that at least 20% of those in the sample will be retired?

d) what is the probability that between 15% and 25% of those in the sample will be retired?