# Statistics and Economics question

Data on the 30 largest stock and balanced funds provided one year and five year percentage returns for the period ending March 31, 2000 (The Wall Street Journal, April 10, 2000). Suppose we consider a one year return in excess of 50% to be high and a five year return in excess of 300% to be high. Nine of the fund had one year returns in excess of 50% and seven of the funds had five year returns in excess of 300%, and five of the funds had both one year returns in excess of 50% and five year returns in excess of 300%

1. What is the probability of a high one year return and what is the probability of a high five year return?
2. What is the probability of both a high one year return and a high five year return?
3. What is the probability of neither a high one year return nor a high five year return?

The Dallas IRS auditing staff, concerned with identifying potentially fraudulent tax returns, believe that the probability of finding a fraudulent return given that the return contains deductions for contributions exceeding the IRS standard is .20. Given that the deductions for contributions do not exceed the IRS standard, the probability of a fraudulent return decreases to .02. If 8% of all returns exceed the IRS standard for deductions due to contributions, what is the best estimate of the percentage of fraudulent returns?

Must show any calculations, facts or reasoning as to how you came up with the answers. Work must be done on excel spreadsheet; work must be original. All questions must be answered