Question: An investor has invested in nine different investments. The dollar returns on the different investments are probabilistically independent, and each return follows a normal distribution with mean $50,000 and standard deviation $10,000.
a. There is a 1% chance that the total return on the nine investments is less than what value? (Use the fact that the sum of independent normal random variables is normally distributed, with mean equal to the sum of the individual means and variance equal to the sum of the individual variances.)
b. What is the probability that the investor's total return is between $400,000 and $520,000?