Answered: a. Exactly 11 of them major in STEM.…

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

26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 49 college students are randomly selected, find the probability that

a. Exactly 11 of them major in STEM.
b. At most 16 of them major in STEM.
c. At least 15 of them major in STEM.
d. Between 7 and 11 (including 7 and 11) of them major in STEM.

Expert Solution

Step 1

The Binomial probability distribution is:

$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) {(p)}^{x} {(1 - p)}^{n - x}$

In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.

Let X be the major in STEM which follows binomial distribution with sample size 49, and probability of success 0.26.

The probability that exactly 11 of them major in STEM is,

$\begin{array}{rcl} P (X = 11) & = & (\begin{matrix} 49 \\ 11 \end{matrix}) {(0.26)}^{11} {(1 - 0.26)}^{49 - 11} \\ = & 0.1148 \end{array}$

Thus, the probability that exactly 11 of them major in STEM is 0.1148.

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