In its October 12, 1992. issue. The Milwaukee Journal published the results of an Ogilvy, Adams, and Rinehart poll of 1,250 American investors that was conducted in early October 1992. The poll investigated the stock market's appeal to investors five years after the market suffered its biggest one-day decline (in 1987).
Assume that 50 percent of all American investors in 1992 found the stock market less attractive than it was in 1987 (that is, p = .5). Find the probability that the sample proportion obtained from the sample of 1,250 investors would be
a. Within 4 percentage points of the population proportion-that is, find P(46 ≤ .54).
b. Within 2 percentage points of the population proportion.
c. Within 1 percentage point of the population proportion.
d. Based on these probabilities, would it be reasonable to claim a ±2 percentage point margin of error? A ± 1 percentage point margin of error? Explain.