For the population of people who suffer occasionally from migraine headaches, suppose that p = 0.60 is the proportion who get some relief from their symptoms by taking ibuprofen.
(a) Let X be the number of individuals in a simple random sample of size 50 from this population who get some relief by taking ibuprofen, and let pˆ be the sample proportion. Find the probability that the value of pˆ is in the interval (0.55, 0.65).
(b) Repeat part (a) assuming that a sample of size 200 is used instead of a sample of size 50.