A simple random sample of size $n$ is drawn from a population that is normally distributed. The sample mean, $\stackrel{}{x},$ is found to be $105,$ and the sample

standard deviation, $s,$ is found to be $12.$

$($a$)$ Construct a $96\%$ confidence interval about $$ if the sample size, $n,$ is $22.$

$($b$)$ Construct a $96\%$ confidence interval about $$ if the sample size, $n,$ is $13.$

$($c$)$ Construct a $95\%$ confidence interval about $$ if the sample size, $n,$ is $22.$

$($d$)$ Should the confidence intervals in parts $($a$)-($c$)$ have been computed if the population had not been normally distributed?