Amanda has 30 years to save for her retirement. At the beginning of each year, she puts a fixed amount into her retirement account. At any point in time, all of Amanda’s retirement funds are tied up in the stock market. Historically the fund has had normally-distributed returns with a mean of 9.5% and a standard deviation of 5%. She assumes that the historical distribution will hold for the next 30 years. She wants to estimate the probability of meeting her goal of having at least $1 million for retirement. Assume that if Amanda reaches her goal before 30 years, she will stop investing and retire at that point. She wants to compare the probability for 3 different annual investment amounts: $4,000, $5,000 and $6,000.