The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of $66$ minutes and a standard deviation of $18$ minutes. Suppose one person at the hot springs is randomly chosen. Let X $=$ the amount of time that person spent at Grover Hot Springs $.$ Round all answers to $4$ decimal places where possible.

a$.$ What is the distribution of X$?$ X ~ N$($

$,$

$)$

b$.$ Find the probability that a randomly selected person at the hot springs stays longer then $83$ minutes.

c$.$ The park service is considering offering a discount for the $5\%$ of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount?

minutes.

d$.$ Find the Inter Quartile Range $($IQR$)$ for time spent at the hot springs.