Question 1:

analyze past loss data and find mean (average) losses equal to $4 million per year with the standard deviation of $300,000. The data are distributed normally. The reserve fund your company sets aside is $4,300,000. What is the probability that losses will exceed the amount of the reserve fund?

Question 2:

Your analysis shows that ABC’s losses in a given year are subject to normal distribution with expected value of losses equal to $2,000,000 and standard deviation of $200,000. ABC plans to set up a reserve fund for the potential losses. ABC wants to have 97.5% confidence that losses will not exceed the amount of the reserve fund. To achieve this goal, what is the minimum amount you should suggest Company ABC to put into this reserve fund?