An insurer has a pool of identical policyholders each with a potential claim that fits the ideal

characteristics of insurability. There are $10,000$ policyholders in the pool. Any single

policyholder has an expected claim of $10$ and the claim$$s standard deviation is $2.$ The insurer

collects premiums at the beginning of the year, and pays claims at the end of the year.

Premium is $9\mathrm{.}5$ per insurer. The insurer invests premiums at an annual rate of $5\mathrm{.}68$ percent.

What is the probability $($a very close approximation will suffice$)$ that the insurer will not

have sufficient money to pay claims?