Question

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 60 minutes and a standard deviation of 17 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 68 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

Answer 1

I a) xNN160,17) b) Probabicity selected rupy that that a randomly person at the hot spring than 68 minutes. stays longer P(x768) = P7 66780 P1220147) -0.3192 The 2-score = l. u 7.58 x = letzo - 60-178 1.4758 9 = 34.9114 The 29th percentile z-sore =-0.6745 x = litzo=60-0.6745 17 Q = 48.8333 pecentice Z- Score = 0.6745 75th x = lutzo 60+0.6745 X 17 O3 = 71.46657 03-8, = 2 2.9330 IQR