Question
Piverlool FC sells player jerseys at random prices. The price of a Sohamed Malah jersey is normally distributed with mean $\$\mu_1$ and standard deviation $\$\sigma_1$. The price of a Madio Sane jersey is normally distributed with mean $\$\mu_2$ and standard deviation $\$\sigma_2$, independent of Malah jerseys. Ben wants to be $(100-\alpha)\%$ sure that he can purchase both jerseys. How much money should Ben bring with him if $\mu_1 = 60, \mu_2 = 75, \sigma_1 = 12, \sigma_2 = 16$ and $\alpha = 5$? Use the values $\Phi^{-1}(0.95) = 1.65$ and/or $\Phi^{-1}(0.975) = 1.96$. If necessary, round to the nearest dollar.