The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 61 minutes and a standard deviation of 15 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 84 minutes.

c. The park service is considering offering a discount for the 7% 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.
Q1: minutes
Q3: minutes
IQR: minutes