Estimate the probability that the loss will be less than $40,000 and the probability that the loss will be greater than $70,000.

The actuaries for an insurance company represent the total losses experienced during a week as follows: Let N represent the number of policies that experience a loss during the week, and Z1,Z2, .be independent random variables that have the same distribution representing the amount of each loss. Then the total losses for the weelk are: Using probability theory, one can show that if N and Z1,z2.. are statistically independent, the expected value of X is: E(X)E(N) E(Z) Thus, under these assumptions, it is easy to compute the mean loss during a week; however, it is not so easy to establish the probability distribution of the total loss. The actuaries for an insurance company represent the total losses experienced during a week as follows: Let N represent the number of policies that experience a loss during the week, and Z1,Z2, .be independent random variables that have the same distribution representing the amount of each loss. Then the total losses for the weelk are: Using probability theory, one can show that if N and Z1,z2.. are statistically independent, the expected value of X is: E(X)E(N) E(Z) Thus, under these assumptions, it is easy to compute the mean loss during a week; however, it is not so easy to establish the probability distribution of the total loss