Answered: A normal distribution has a mean of 13…

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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Question

A normal distribution has a mean of 13 and a standard deviation of 3. Use the 68-95-99.7 rule to find the percentage of values in the distribution above 16.

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.

Expert Solution

Step 1

Introduction

The normal distribution demonstrates a balanced projection of observations around its average value, with the standard deviation operating as the defining factor of the curve's comprehensiveness. The "bell curve" has been employed to adequately display it. To estimate probable possibilities in a normal curve, the empirical rule is being used. This might be employed, for reference, by a researcher to establish what percentage of the cases fall within every standard deviation.

In the given scenario, the population parameters (mean and standard deviation) of normally distributed data were given. We will use an empirical rule to find the percentage of getting a value above 16.