When $23$ athletes were randomly selected; it was found that they had averaged $15$ hours of workout per week. The population standard deviation is $2$ hours. The $90\%$ confidence interval, of the average number of workout hours for all athletes $($assuming that the population is normally distributed$),$ is:

a$)(14\mathrm{.}31,16\mathrm{.}69$

b$)(14\mathrm{.}31,14\mathrm{.}69)$

c$)(14\mathrm{.}31,15\mathrm{.}69)$

d$)(14\mathrm{.}31,17\mathrm{.}69)$