The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 70minutes and a standard deviation of 14 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 placeswhere 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 92 minutes.c. The park service is considering offering a discount for the 6% of their patrons who spend the least timeat the hot springs. What is the longest amount of time a patron can spend at the hot springs and stillreceive the discount?minutes.d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.Q1:minutesQ3:minutesIQR:minutes

Answered: The amount of time that people spend at…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 70
minutes and a standard deviation of 14 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 92 minutes.
c. The park service is considering offering a discount for the 6% 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

Expert Solution

Step 1

Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get the remaining sub-parts solved, please repost the complete question and mention the sub-parts to be solved.

Since the variable "the amount of time spent in the Grover hot spring" (i.e., denoted by $X$ ) is claimed to be distributed normally with the given mean and standard deviation of 70 minutes (i.e., $μ = 70$ ) and 14 minutes (i.e., $σ = 14$ ) respectively. For a random amount of time, that is spent on the hot spring, the z-score is given as:

$z = \frac{X - μ}{σ}$