Discuss the below:
Q1: It has been estimated that 17.0% of mutual fund shareholder are retired persons. Assuming the population proportion to be π = 0.17 and that a simple random sample of 400 shareholders ha 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?
Q2: A simple random sample with n = 200 is drawn from a binomial process in which π= 0.6. Determine the following probabilities for p = the proportion of successes
a. P(0.50 ≤ p)
b. P(0.65≤p≤0.70)
c. P(p ≥0.70)