Answered: uess that the people reside in a city…

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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Question

Guess that the people reside in a city have a mean score of 50 and a standard deviation of 7 on a measure of concern about the environment. Assume that these scores are normally distributed.

1. If a person is randomly selected from that city then what is the probability that he or she has a score below 25?

b. If a person is randomly selected from that city then what is the probability that he or she has a score above 52?

c. If a person is randomly selected from that city then what is the probability that his/her score is between 30 and 40?

Expert Solution

Step 1

The provided information are:

Population mean ( $μ$ ) = 50

Population standard deviation ( $σ$ ) = 7

Step 2

Consider, X be the random variable that shows the scores is following the normal distribution with mean = 50 and standard deviation = 7.

(a)

The probability that randomly chosen person has score below 25 could be calculated as:

$\begin{array}{rcl} P (X & < & 25) = P (\frac{x - μ}{σ} < \frac{25 - μ}{σ}) \\ = & P (Z < \frac{25 - 50}{7}) \\ = & P (Z < - 3.57) \\ = & 0.0002 \end{array}$

Thus, the required probability is 0.0002.

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