Given a normal distribution with $=100$ and $=10,$ and given you select a sample of $n=4,$ complete parts $($a$)$ through $($d$).$

a$.$ What is the probability that $\stackrel{}{x}$ is less than $90?$

$($Type an integer or decimal rounded to four decimal places as needed.$)$

b$.$ What is the probability that $\stackrel{}{x}$ is between $90$ and $90\mathrm{.}5?$

$($Type an integer or decimal rounded to four decimal places as needed.$)$