Twenty-five percent of the employees of a large company are minorities.A random sample of 7 employees is selected.a. What is the probability that the sample contains exactly 4minorities?b. What is the probability that the sample contains not more than 2minorities?c. What is the standard deviation of the minorities?

Answered: a. What is the probability that the…

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

Twenty-five percent of the employees of a large company are minorities.
A random sample of 7 employees is selected.
a. What is the probability that the sample contains exactly 4
minorities?
b. What is the probability that the sample contains not more than 2
minorities?
c. What is the standard deviation of the minorities?

Expert Solution

Step 1: Determine the given data in the question

Let X be the random variable that a number of the employees are minorities.

Given that,

No. of employees $left parenthesis n right parenthesis equals 7$

Proportion of employees are minorities $left parenthesis p right parenthesis equals 25 percent sign equals 0.25$

$q equals 1 minus p equals 1 minus 0.25 equals 0.75$

The pmf of X=x is,

$P left parenthesis X equals x right parenthesis equals n subscript C subscript x end subscript p to the power of x q to the power of n minus x end exponent comma x equals 0 comma 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 equals 7 subscript C subscript x end subscript 0.25 to the power of x 0.75 to the power of 7 minus x end exponent$