Question: Applying to college. You ask an SRS of 1500 college students whether they applied for admission to any other college. Suppose that in fact 35% of all college students applied to colleges besides the one they are attending. (That's close to the truth.) The sampling distribution of the proportion p^ of your sample who say "Yes" is approximately Normal with mean 0.35 and standard deviation 0.01. Sketch this Normal curve and use it to answer the following questions.
(a) Explain in simple language what the sampling distribution tells us about the results of our sample.
(b) What percentage of many samples would have a p^ larger than 0.37? (Use the 68-95-99.7 rule.) Explain in simple language why this percentage is the probability of an outcome larger than 0.37.
(c) What is the probability that your sample will have a p^ less than 0.33?
(d) Use Rule D: what is the probability that your sample result will be either less than 0.33 or greater than 0.35?