Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A sample of $300$ students is taken. Of the students surveyed, $50$ were music students, while $250$ were not. Ninetyseven were on the honor roll, while $203$ were not. If we assume being a music student and being on the honor roll are independent events, what is the expected number of music students who are also on the honor roll?

Around $16$ kids from a sample are likely to be music students who are also on the honour roll.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Given information

Given in the question that, A sample of $300$ students is taken. Of the students surveyed, $50$ were music students, while $250$ were not. Ninetyseven were on the honor roll, while $203$ were not. If we assume being a music student and being on the honor roll are independent events. We need to find the expected number of music students who are also on the honor roll if we assume being a music student and being on the honor roll are independent events.

Explanation

A total of $300$ pupils are chosen as a sample. $50$ of the students polled were music students, whereas the other $250$ were not. Ninety-seven students were on the honour roll, while the remaining $203$ were not.

Calculation:

Let the random variable $X$ be defined as

$X =$ Expected number of students on the honour roll who are also music students.

Let $A$ represent the fact that the student is a music student, and $B$ represent the fact that he or she is also on honour roll. We have the following condition if both occurrences $A$ and $B$ are independent events:

$P (A A N D B) = P (A) \cdot P (B)$

We have,

$P (A) = \frac{50}{300}$

$P (B) = \frac{97}{300}$

$\Rightarrow \frac{X}{300} = \frac{50}{300} \times \frac{97}{300}$

localid="1653556696458" $\Rightarrow X = \frac{4850}{300} = 16.17 \approx 16$

$∴ X = 16$

Business Type	Number in class	Observed Number that recycles one commodity	Expected number that recycles one commodity
office	$35$	$19$	$17.5$
Retail/Wholesale	$48$	$27$	$24$
Food/Restaurants	$53$	$35$	$26.5$
Manufacturing/Medical	$52$	$21$	$26$
Hotel/Mixed	$24$	$9$	$12$

Find Study Materials for

Create Study Materials

Select your language

Introductory Statistics

Answers without the blur.

Short Answer

Step by Step Solution

Given information

Explanation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Introductory Statistics

Answers without the blur.

Short Answer

Step by Step Solution

Given information

Explanation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths