0. Deadly Movie Stunts Incorporated (DMSI) offers a group accidental death life policy to each of its twenty employees. Each employee is insured for twice their annual salary. The actuarial data on the twenty employees is as follows.

   • There are 4 employees each with an annual salary of $50,000 and each with an annual probability of accidental death equal to 0.015.

   • There are 7 employees each with an annual salary of $70,000 and each with an annual probability of accidental death equal to 0.02.

   • There are 4 employees each with an annual salary of $85,000 and each with an annual probability of accidental death equal to 0.03.

   • There are 5 employees each with an annual salary of $100,000 and each with an annual probability of accidental death equal to 0.04.

     The insurer addes a 25% relative loading to the net premium. (In other words, the insurer charges DMSI 125% of the expected payment as the premium for the group accidental death coverage.)

     (1) Based on the lognormal approximation, what is the probability that the insurer will lose money writing this group policy to DMSI?

     (2) Based on the normal approximation, what is the probability that the insurer will lose more than $10,000 writing this group policy to DMSI?