1. According to Money, in the year prior to March 2007, the average return for ?rms of the S&P 500 was 13.1%.9 Assume that the standard deviation of returns was 1.2%. If a random sample of 36 companies in the S&P 500 is selected, what is the probability that their average return for this period will be between 12% and 15%?
2. An economist wishes to estimate the average family income in a certain pop- ulation. The population standard deviation is known to be $4,500, and the economist uses a random sample of size n = 225. What is the probability that the sample mean will fall within $800 of the population mean?
3. When sampling is done for the proportion of defective items in a large ship- ment, where the population proportion is 0.18 and the sample size is 200, what is the probability that the sample proportion will be at least 0.20?
4. A study of the investment industry claims that 58% of all mutual funds out- performed the stock market as a whole last year. An analyst wants to test this claim and obtains a random sample of 250 mutual funds. The analyst ?nds that only 123 of the funds outperformed the market during the year. Determine the probability that another random sample would lead to a sample proportion as low as or lower than the one obtained by the analyst, assuming the proportion of all mutual funds that out performed the market is indeed 0.58.