### Understanding Z-Scores in Standardized Exams#### Problem Statement:_**On a standardized exam, the scores are normally distributed with a mean of 140 and a standard deviation of 20. Find the z-score of a person who scored 140 on the exam.**_---#### Explanation:1. **Mean (μ)**: This is the average score of the exam, which is given as 140.2. **Standard Deviation (σ)**: This measures the dispersion of the exam scores from the mean, which is given as 20.3. **Individual Score (X)**: The score of the person for whom we are calculating the z-score, which is 140 in this case.A z-score tells us how many standard deviations a particular score is from the mean. The formula to calculate the z-score is:\[ Z = \frac{X - \mu}{σ} \]Where:- $ Z $ is the z-score,- $ X $ is the individual score,- $ \mu $ is the mean,- $ σ $ is the standard deviation.#### Calculation:Plugging in the values from the problem statement:\[ Z = \frac{140 - 140}{20} \]\[ Z = \frac{0}{20} \]\[ Z = 0 \]The z-score for a person who scored 140 on the exam is 0. A z-score of 0 indicates that the person's score is exactly equal to the mean.---#### Interactive Query:To aid your understanding, please input your answer below.**Answer:** Submit Answer---This interactive exercise helps reinforce the concept of z-scores and how they relate to the normal distribution of exam scores.#### Additional Resources:- Watch help video- [Privacy Policy](#) | [Terms of Service](#)

mean = 140 standard deviation =20

Answered: On a standardized exam, the scores are…

On a standardized exam, the scores are normally distributed with a mean of 140 an a standard deviation of 20. Find the z-score of a person who scored 140 on the exam

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

### Understanding Z-Scores in Standardized Exams

#### Problem Statement:

_**On a standardized exam, the scores are normally distributed with a mean of 140 and a standard deviation of 20. Find the z-score of a person who scored 140 on the exam.**_

---

#### Explanation:

1. **Mean (μ)**: This is the average score of the exam, which is given as 140.
2. **Standard Deviation (σ)**: This measures the dispersion of the exam scores from the mean, which is given as 20.
3. **Individual Score (X)**: The score of the person for whom we are calculating the z-score, which is 140 in this case.

A z-score tells us how many standard deviations a particular score is from the mean. The formula to calculate the z-score is:

\[ Z = \frac{X - \mu}{σ} \]

Where:
- $ Z $ is the z-score,
- $ X $ is the individual score,
- $ \mu $ is the mean,
- $ σ $ is the standard deviation.

#### Calculation:

Plugging in the values from the problem statement:

\[ Z = \frac{140 - 140}{20} \]

\[ Z = \frac{0}{20} \]

\[ Z = 0 \]

The z-score for a person who scored 140 on the exam is 0. A z-score of 0 indicates that the person's score is exactly equal to the mean.

---

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