The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 68 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? \[ X \sim N(68, 15) \] b. Find the probability that a randomly selected person at the hot springs stays longer than 64 minutes. \[ \text{Probability} = 0.6051 \] 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? \[ \text{Time} = \_ \_ \_ \_ \text{ minutes} \] d. Find the Interquartile Range (IQR) for time spent at the hot springs. - Q1: \_ \_ \_ \_ \text{ minutes} - Q3: \_ \_ \_ \_ \text{ minutes} - IQR: \_ \_ \_ \_ \text{ minutes} Hint: Enter an integer or decimal number, accurate to at least 4 decimal places.

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