The Fullerton Arboretum is a wonderful place to visit. It is located on the CSUF campus. The amount oftime spent at the Arboretum is normally distributed with a mean of 70 minutes and a standard deviation of17 minutes. Suppose one person at the Arboretum is randomly selected. Let X = the amount of time thatperson spent at the Fullerton Arboretum. 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 Fullerton Arboretum stays longer then 84minutes.c. The school is considering offering a discount for the 8% of their patrons who spend the least time at theArboretum. What is the longest amount of time a patron can spend at the Arboretum and still receive thediscount?minutes.d. Find the Inter Quartile Range (IQR) for time spent at the Arboretum.Q1:minutesQ3:minutesIQR:minutes

Answered: The Fullerton Arboretum is a wonderful…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Fullerton Arboretum is a wonderful place to visit. It is located on the CSUF campus. The amount of
time spent at the Arboretum is normally distributed with a mean of 70 minutes and a standard deviation of
17 minutes. Suppose one person at the Arboretum is randomly selected. Let X = the amount of time that
person spent at the Fullerton Arboretum. 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 Fullerton Arboretum stays longer then 84
minutes.
c. The school is considering offering a discount for the 8% of their patrons who spend the least time at the
Arboretum. What is the longest amount of time a patron can spend at the Arboretum and still receive the
discount?
minutes.
d. Find the Inter Quartile Range (IQR) for time spent at the Arboretum.
Q1:
minutes
Q3:
minutes
IQR:
minutes

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Solution:

X be the amount of time a person spends at the Fullerton Arboretum.

Also, it is given that the amount of time spent at the Arboretum is normally distributed with a mean of 70 minutes and standard deviation of 17 minutes.

Part a)

X is normally distributed with mean ( $μ$ )70 minutes and standard deviation ( $σ$ )17 minutes.

X ~ N(70, 17)

Part b)

The probability that a randomly selected person at the Fullerton Arboretum stays longer than 84 minutes is required.

That is, P(X > 84) is required.

It can be easily found using MS-Excel as follows:

Type =1-NORMDIST(84, 70, 17, 1) and hit enter. It gives 0.205103.

Rounding it to 4 decimal places, it becomes 0.2051.

Thus, the probability that a randomly selected person at the Fullerton Arboretum stays longer than 84 minutes is 0.2051.

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