Peter has $30,000 to invest in a mutual fund whose annual returns are normally distributed with a mean of 4.81% and standard deviation of 4.48%.

a. Use Excel's Analysis ToolPak, with a seed of 1, to simulate 5,000 trials to estimate the mean balance after one year. (Round intermediate calculations to at least 4 decimal places and your final answer to 2 decimal places.)

b. What is the probability of a balance of $32,800 or more? (Round intermediate calculations to at least 4 decimal places and show your final answer as a percentage point with 2 decimal places.)

c. Compared to another investment option at a fixed annual return of 3% per year, what is the probability of getting at least the same balance from the mutual fund after one year? (Round intermediate calculations to at least 4 decimal places and show your final answer as a percentage point with 2 decimal places.)