18.24 Do you jog? An opinion poll asks an SRS of 1500 adults, “Do you happen to jog?” Suppose (as is approximately correct) that the population proportion who jog is p = 0.15. In a large number of samples, the proportion who answer Yes will be approximately Normally distributed with mean 0.15 and standard deviation 0.009. Sketch this Normal curve and use it to answer the following questions.
(a) What percentage of many samples will have a sample proportion who jog that is 0.15 or less? Explain clearly why this percentage is the probability that is 0.15 or less.
(b) What is the probability that will take a value between 0.141 and 0.159? (Use the 68–95–99.7 rule.)
(c) Now use Rule C for probability: what is the probability that does not lie between 0.141 and 0.159?