OmniSure is a life insurance company. One of the policies it offers is long$-$term care insurance, which is a type of policy that is used to pay for care related to daily living for individuals with chronic illnesses or disabilities.

In a sample of $50$ customers whose policies had paid out recently, the company found that the customers' average age was $80$ years, with a sample standard deviation of $2$ years. Which of the following is the $95\%$ confidence interval for the true mean age of all customers who have this long$-$term care policy?

$79\mathrm{.}4$ to $80\mathrm{.}6$

$77\mathrm{.}7$ to $84\mathrm{.}9$

$79\mathrm{.}2$ to $80\mathrm{.}8$

$79\mathrm{.}6$ to $80\mathrm{.}6$

$79\mathrm{.}9$ to $80\mathrm{.}1$