25. The results for a mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100 points.a.) Suppose that the top 3% of students receive a scholarship. What is the minimum score required to receive this scholarship?b.) The bottom 1.5% of the students must go to summer school. What is the minimum score you would need to stay out of summer school?c.) What are the two scores that will define the middle 50% of the test scores? **Problem 25: Normal Distribution in Test Scores**The results for a mandatory competency test for high school sophomores follow a normal distribution with a mean of 400 and a standard deviation of 100 points.**Questions:**a.) Suppose that the top 3% of students receive a scholarship. What is the minimum score required to receive this scholarship?b.) The bottom 1.5% of the students must go to summer school. What is the minimum score you would need to stay out of summer school?c.) What are the two scores that will define the middle 50% of the test scores?**Explanation:**- ***Mean (µ):*** 400- ***Standard Deviation (σ):*** 100Use these values to calculate z-scores and determine the required scores for the specified percentages outlined in the questions.

Mean()=400standard deviation()=100

Answered: 25. The results for a mandatory…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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25. The results for a mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100 points. a.) Suppose that the top 3% of students receive a scholarship. What is the minimum score required to receive this scholarship? b.) The bottom 1.5% of the students must go to summer school. What is the minimum score you would need to stay out of summer school? c.) What are the two scores that will define the middle 50% of the test scores?

**Problem 25: Normal Distribution in Test Scores**

The results for a mandatory competency test for high school sophomores follow a normal distribution with a mean of 400 and a standard deviation of 100 points.

**Questions:**

a.) Suppose that the top 3% of students receive a scholarship. What is the minimum score required to receive this scholarship?

b.) The bottom 1.5% of the students must go to summer school. What is the minimum score you would need to stay out of summer school?

c.) What are the two scores that will define the middle 50% of the test scores?

**Explanation:**

- ***Mean (µ):*** 400
- ***Standard Deviation (σ):*** 100

Use these values to calculate z-scores and determine the required scores for the specified percentages outlined in the questions.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Mean( $straight mu$ )=400

standard deviation( $straight sigma$ )=100

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