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Q. 33

Expert-verified
Found in: Page 386

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# About what percent of $x$ values lie between the second and third standard deviations (both sides)?

Approximately $4.7%$ of $x$ values lies between the second and third standard deviation

See the step by step solution

## Step 1: Concept Introduction

The empirical rule additionally alluded to as the three-sigma rule or 68-95-99.7 rule, is a factual decision that expresses that for a normal distribution, practically totally noticed information will fall inside three standard deviations of the mean or normal .

## Step 2: Explanation

The Empirical Rule expresses that $99.7%$of information noticed observing an normal distribution exists in $3$ standard deviations of the mean. Under this standard, $68%$ of the information falls inside one standard deviation, $95%$percent inside two standard deviations, and $99.7%$ inside three standard deviations from the mean.

Therefore, the percentage of $x$ values from normal distribution lie between second and third standard deviation will be:

$=99.7%-95%$

localid="1648289831679" $=4.7%$