MTH128 Chapter 8 samples sizes

1) You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=74.3. You would like to be 90% confident that your estimate is within 4 of the true population mean. How large of a sample size is required? 2) SAT scores are distributed with a mean of 1,500 and a standard deviation of 282. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your confidence interval to 50 points with 85 percent confidence, how many students should you sample? (Round up to a whole number of students.) 3) A pollster wishes to estimate, with 95% confidence, the proportion of people who who believe that the United Nations is doing a good job of solving problems. Find the minimum sample size necessary to achieve a margin of error of less than 3%. Assuming no previous estimates are available. Round your answer up to the next integer. Assuming a previous estimate of 0.35. Round your answer up to the next integer.