# 2-6: The Normal Probability Distribution### ExampleIn a large world history class, the distribution of final exam grades is approximately normal. The mean score is 78 with a standard deviation of 6.#### Diagram ExplanationThe diagram illustrates a normal distribution curve centered around the mean of 78. Vertical lines are drawn at intervals indicating one, two, and three standard deviations from the mean on both sides of the curve.#### Data Summary- **68% of the grades are within 1 standard deviation of the mean:** between ____ and ____.- **95% of the grades are within 2 standard deviations of the mean:** between ____ and ____.- **99.7% of the grades are within 3 standard deviations of the mean:** between ____ and ____.### Question1. **What percentage of students scored below 85?** a. Draw the normal curve and shade the related area. b. Find the z-value that corresponds to a score of 85. c. Approximate this percentage.

In this context, it is given that the mean score is 78 with a standard deviation of 6. Grades within…

Answered: 1. What percentage of students scored…

1. What percentage of students scored below 85? a. Draw the normal curve and shade the related area. b. Find the z-value that corresponds to a score of 85. C. Approximate this percentage.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

# 2-6: The Normal Probability Distribution

### Example

In a large world history class, the distribution of final exam grades is approximately normal. The mean score is 78 with a standard deviation of 6.

#### Diagram Explanation
The diagram illustrates a normal distribution curve centered around the mean of 78. Vertical lines are drawn at intervals indicating one, two, and three standard deviations from the mean on both sides of the curve.

#### Data Summary
- **68% of the grades are within 1 standard deviation of the mean:** between ____ and ____.
- **95% of the grades are within 2 standard deviations of the mean:** between ____ and ____.
- **99.7% of the grades are within 3 standard deviations of the mean:** between ____ and ____.

### Question

1. **What percentage of students scored below 85?**

a. Draw the normal curve and shade the related area.

b. Find the z-value that corresponds to a score of 85.

c. Approximate this percentage.

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