Suppose that scores on a particular test are normally distributed with a mean of 140 and a standard deviation of 16. What is the minimum score needed to be in the top 2% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
Suppose that scores on a particular test are normally distributed with a mean of 140 and a standard deviation of 16. What is the minimum score needed to be in the top 2% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
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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![**Transcription for Educational Website**
*Problem Statement:*
Suppose that scores on a particular test are normally distributed with a mean of 140 and a standard deviation of 16. What is the minimum score needed to be in the top 2% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
*Explanation:*
To find the minimum score needed to be in the top 2%:
1. Determine the z-score that corresponds to the top 2% of a normal distribution.
2. Use the z-score formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \(X\) is the score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
3. Rearrange the formula to solve for \(X\):
\[
X = z\sigma + \mu
\]
4. Use statistical tables or software to find the z-score for the top 2% and calculate \(X\).
*Interactive Elements:*
- **Input Box:** For entering the calculated score.
- **Buttons:**
- **X:** Clears the input box.
- **Circular Arrow:** Resets the problem.
- **Question Mark:** Provides a hint or additional help.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe53f16ab-a658-43ea-87b0-0607d7296018%2F59bd112e-4760-4362-8bc3-63420fdf3750%2Fjke5spm_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
*Problem Statement:*
Suppose that scores on a particular test are normally distributed with a mean of 140 and a standard deviation of 16. What is the minimum score needed to be in the top 2% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
*Explanation:*
To find the minimum score needed to be in the top 2%:
1. Determine the z-score that corresponds to the top 2% of a normal distribution.
2. Use the z-score formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \(X\) is the score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
3. Rearrange the formula to solve for \(X\):
\[
X = z\sigma + \mu
\]
4. Use statistical tables or software to find the z-score for the top 2% and calculate \(X\).
*Interactive Elements:*
- **Input Box:** For entering the calculated score.
- **Buttons:**
- **X:** Clears the input box.
- **Circular Arrow:** Resets the problem.
- **Question Mark:** Provides a hint or additional help.
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