The Gallup Poll once asked a random sample of 1470 adults, “Do you happen to jog?" Suppose that in fact 25% of all adults jog
(a) Find the mean and standard deviation of the sampling distribution of the proportion of the sample who jog. (Assume
the sample is an SRS.)
(b) Explain why you can use the formula for the standard deviation of the sampling distribution in this setting.
(C) Check that you can use the normal approximation for the sampling distribution.
(d) Find the probability that between 22% and 28% of the sample jog.
(e) What sample size would be required to reduce the standard deviation of the sample proportion to one-third the value
you found in (a)?