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Given in the question that, the risk of insuring one person's life is reduced if we insure many people. Given that we insure two 21 year-old males and their ages at death are independent. Let $X_{1}and{X}_2$be the insurer's income from the two insurance policies. The insurer's average income W on the two policies is given by

$W=\frac{X_1+X_2}{2}=0.5X_1+0.5X_2$

We have to Find the mean and standard deviation of $W$.

Let's consider $X$as the random variable which shows the amount a life insurance company earns on a $5$year term life policy.

The mean and standard deviation of $X$are:

$$\begin{gathered} {渭}_X=303.35 \\ {蟽}_X=9707.57 \end{gathered}$$

Let's find the mean of $W$

localid="1649871962725" $$\begin{gathered} {渭}_W=0.5{渭}_{X_1}+0.5{渭}_{X_2} \\ =0.5脳303.35+0.5脳303.35 \\ =303.35 \end{gathered}$$

Now, find the standard deviation of $W$

localid="1649872007295" $$\begin{gathered} {蟽}_W=\sqrt{0.25脳9707.{57}^2+0.25脳9707.{57}^2} \\ =\sqrt{47118457.65} \\ =6864.29 \end{gathered}$$