The time intervals between successive repairs of a system generate an ordinary renewal process \(\left\{Y_{1}, Y_{2}, \ldots\right\}\) with typical cycle length \(Y\). The costs of repairs are mutually independent and independent of \(\left\{Y_{1}, Y_{2}, \ldots\right\}\).

Let \(M\) be the typical repair cost and \[\begin{gathered} \mu=E(Y)=180 \text { [days] and } \sigma=\sqrt{\operatorname{Var}(Y)}=30 \\ u=E(M)=200[\$] \text { and } \sqrt{\operatorname{Var}(M)}=40 \end{gathered}\]
Determine approximately the probabilities that (1) the total repair costs arising in [0, 3600 days] do not exceed \(\$ 4500\), and (2) a total repair cost of \(\$ 3000\) is not exceeded before 2200 days.