The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62 minutes and a standard deviation of 16 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(
62
,
16
)

b. Find the probability that a randomly selected person at the hot springs stays longer then 75 minutes.
0.2083


c. The park service is considering offering a discount for the 8% 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.