Question $1$

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?