A test consists of 230 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers? Round the answer to the nearest hundredth. .... O A. 0.00 O B. 7.58 OC. 10.72 O D. 2.00
A test consists of 230 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers? Round the answer to the nearest hundredth. .... O A. 0.00 O B. 7.58 OC. 10.72 O D. 2.00
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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![The image presents a question regarding statistics:
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**Question:**
A test consists of 230 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers? Round the answer to the nearest hundredth.
**Answer Choices:**
- A. 0.00
- B. 7.58
- C. 10.72
- D. 2.00
**Navigation:**
A "Next" button is visible in the bottom right corner of the screen.
---
Explanation for Educational Context:
In this scenario, the student is guessing on a 230-question true or false test. To find the standard deviation of the number of correct answers when guessing on each question, you can use the formula for the standard deviation of a binomial distribution:
\[ \sigma = \sqrt{n \cdot p \cdot (1-p)} \]
where \( n \) is the number of trials (questions), and \( p \) is the probability of getting a question correct (for true or false, \( p = 0.5 \)).
Applying these numbers:
\[ \sigma = \sqrt{230 \cdot 0.5 \cdot (1-0.5)} = \sqrt{230 \cdot 0.5 \cdot 0.5} = \sqrt{230 \cdot 0.25} = \sqrt{57.5} \]
Therefore, the standard deviation rounded to the nearest hundredth is approximately 7.58, corresponding to option B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9e160d3-5f97-49cf-bcaa-ed4b67fa5615%2F158dcdd6-eaec-41b8-bc1a-427d46d6e202%2F7qhcj3q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a question regarding statistics:
---
**Question:**
A test consists of 230 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers? Round the answer to the nearest hundredth.
**Answer Choices:**
- A. 0.00
- B. 7.58
- C. 10.72
- D. 2.00
**Navigation:**
A "Next" button is visible in the bottom right corner of the screen.
---
Explanation for Educational Context:
In this scenario, the student is guessing on a 230-question true or false test. To find the standard deviation of the number of correct answers when guessing on each question, you can use the formula for the standard deviation of a binomial distribution:
\[ \sigma = \sqrt{n \cdot p \cdot (1-p)} \]
where \( n \) is the number of trials (questions), and \( p \) is the probability of getting a question correct (for true or false, \( p = 0.5 \)).
Applying these numbers:
\[ \sigma = \sqrt{230 \cdot 0.5 \cdot (1-0.5)} = \sqrt{230 \cdot 0.5 \cdot 0.5} = \sqrt{230 \cdot 0.25} = \sqrt{57.5} \]
Therefore, the standard deviation rounded to the nearest hundredth is approximately 7.58, corresponding to option B.
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