I am trying to get into the insurance business. As a starter, I am going to sell the 2019 Kelly MBA class an unemployment insurance policy that will pay a student $100k if they don't get a job by the end of the program (by graduation time). From years and years of observing this program, I figured that the probability that a student does not get a job by the end of program is 0.5%. Based on this number I decided to sell each policy for $850.

(a) (15 points) From the perspective of my insurance business, is that a good price? Justify your answer from the expected profit for each policy.

(b) (15 points) The standard deviation for the payout of one policy is approximately $7k. What is the probability (approximately) that I will lose money by graduation time if I was able to sell this policy to 1000 students in the 2019 class?