Problem

An I.R.S. agent audits 20 income tax returns every month. These returns are carefully selected by the I.R.S. for suspicion of fraud. The probability that any one of the selected returns is found to be fraudulent by the I.R.S. agent is 0.25. Each of the income tax returns is independent of the other income tax returns.

3a) What is the probability that the I.R.S. agent finds exactly 5 fraudulent tax returns out of the 20 tax returns that he audits this month? (WORK REQUIRED

3b) What is the probability that the I.R.S. agent finds at most 3 fraudulent tax returns out of the 20 tax returns that he audits this month? (WORK REQUIRED

3c) What is the probability that the I.R.S. agent finds between 10 and 15 (inclusive) fraudulent tax returns out of the 20 tax returns that he audits this month? (WORK REQUIRED

Problem

Based on daily stock prices for the last several years, the rates of return per share for SWA (Southwest Airlines) and United Airlines are both normally distributed. The mean and standard deviation for SWA rate of return are 2.5% and 1% respectively. The mean and standard deviation for United Airlines rate of return are -4.5% and 2% respectively. Assume the rates of return per share for SWA and United Airlines are statistically independent.

4a) There is a 0.2 probability that the rate of return for SWA will be greater than what value? (WORK REQUIRED

4b) Determine the probability the rate of return for United will be positive. (WORK REQUIRED

4c) Determine the probability that the rates of return for both stocks will be positive. (WORK REQUIRED