A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. The results of the survey are summarized in the following table. Preferred Fitness Area Spinning Room Climbing Wall Ellipticals Year 1-2 37 81 20 Class Level Year 3-4 71 86 47 Graduate Student 81 55 22 What is the probability that a randomly selected student is interested in a spinning room given that they are a graduate student?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
### Multiple Choice

Please select the correct answer from the options below:

1. ○ 0.513
2. ○ 0.381
3. ○ 0.684
4. ○ 0.129

Each option is marked with a circular radio button, allowing for only one selection. Please consider your answer carefully before making a choice.
Transcribed Image Text:### Multiple Choice Please select the correct answer from the options below: 1. ○ 0.513 2. ○ 0.381 3. ○ 0.684 4. ○ 0.129 Each option is marked with a circular radio button, allowing for only one selection. Please consider your answer carefully before making a choice.
### University Fitness Area Survey Results

A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. The survey results are summarized in the table below:

| **Class Level**       | **Preferred Fitness Area** |                         |                          |
|-----------------------|--------------------------- |-------------------------|------------------------- |
|                       | **Spinning Room**          | **Climbing Wall**       | **Ellipticals**          |
| **Year 1-2**          | 37                         | 81                      | 20                       |
| **Year 3-4**          | 71                         | 86                      | 47                       |
| **Graduate Student**  | 81                         | 55                      | 22                       |

### Probability Calculation

**Question:** What is the probability that a randomly selected student is interested in a spinning room given that they are a graduate student?

To find this probability, use the conditional probability formula:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Where:
- \( A \) is the event that a student is interested in a spinning room.
- \( B \) is the event that a student is a graduate student.
- \( P(A \cap B) \) is the joint probability that the student is a graduate student and is interested in a spinning room.
- \( P(B) \) is the probability that the student is a graduate student.

From the table:
- There are 81 graduate students interested in the spinning room.
- The total number of graduate students surveyed is \( 81 + 55 + 22 = 158 \).

Thus, the probability \( P(A|B) \) is:

\[ P(A|B) = \frac{81}{158} \]

This gives the probability that a randomly selected graduate student is interested in the spinning room.
Transcribed Image Text:### University Fitness Area Survey Results A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. The survey results are summarized in the table below: | **Class Level** | **Preferred Fitness Area** | | | |-----------------------|--------------------------- |-------------------------|------------------------- | | | **Spinning Room** | **Climbing Wall** | **Ellipticals** | | **Year 1-2** | 37 | 81 | 20 | | **Year 3-4** | 71 | 86 | 47 | | **Graduate Student** | 81 | 55 | 22 | ### Probability Calculation **Question:** What is the probability that a randomly selected student is interested in a spinning room given that they are a graduate student? To find this probability, use the conditional probability formula: \[ P(A|B) = \frac{P(A \cap B)}{P(B)} \] Where: - \( A \) is the event that a student is interested in a spinning room. - \( B \) is the event that a student is a graduate student. - \( P(A \cap B) \) is the joint probability that the student is a graduate student and is interested in a spinning room. - \( P(B) \) is the probability that the student is a graduate student. From the table: - There are 81 graduate students interested in the spinning room. - The total number of graduate students surveyed is \( 81 + 55 + 22 = 158 \). Thus, the probability \( P(A|B) \) is: \[ P(A|B) = \frac{81}{158} \] This gives the probability that a randomly selected graduate student is interested in the spinning room.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman