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 of your sample who say “Yes” is approximately Normal with mean 0.35 and standard deviation 0.01. Choose the best answer for each problem below. Answers may be use once, more than once or not at all. What percentage of many samples would have a sample proportion less than .335? Use z-score (standard score) to find this answer. What percentage of many samples would have a sample proportion larger than 0.37? (Use the 68–95–99.7 rule.) What is the probability that your sample will have a proportion less than 0.33?

Since it says that σ = 0.01, and it's asking for the percent of the proportion larger than 0.37, they are asking for the percent of the proportion that is 2 standard deviations higher than the mean. Using the 68-95-99.7 rule, we have a total of 5% of data that is more than 2 standard deviations away, but that is on both sides of the mean. Divide that in half to get the total above 0.37. So there should be about 5%/2 = 2.5% of the proportions.

c: Find P(p < 0.33)

0.33 is 2 standard deviations below the mean, so the percentage is 2.5% for similar reasons for part b