Question 10 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 decimat places where possible. %3! a. What is the distribution of X? X ~ N( b. Find the probability that a randomly selected person at the hot springs-stays tonger then 87 minutes. 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 tongest amount of time a patron can spend at the hot springs and still receive the discount? minutes.

MATLAB: An Introduction with Applications
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Question 10
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 ~ N(
b. Find the probability that a randomly selected person at the hot springs stays longer then 87 minutes.
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.
d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.
Q1:
Eminutes
Q3:
minutes
IQR:
minutes
Submit Question
Rain.
16
IOI
&
2$4
5.
L.
8
P
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R T Y U
Transcribed Image Text:Question 10 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 ~ N( b. Find the probability that a randomly selected person at the hot springs stays longer then 87 minutes. 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. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: Eminutes Q3: minutes IQR: minutes Submit Question Rain. 16 IOI & 2$4 5. L. 8 P E R T Y U
Expert Solution
Step 1
We have given that.
 
X~N( μ , ?^2 )
 
μ =68 , ? =15
 
Z-score =( x - μ )/?
 
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