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Q. 33

Expert-verified

Introductory Statistics

Found in: Page 386

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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" $= 4.7 %$

Most popular questions for Math Textbooks

In a normal distribution, x = –2 and z = 6. This tells you that x = –2 is ____ standard deviations to the ____ (right or left) of the mean.

The length of time to find it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. If the mean is significantly greater than the standard deviation, which of the following statements is true?

I. The data cannot follow the uniform distribution.

II. The data cannot follow the exponential distribution..

III. The data cannot follow the normal distribution.

a. I only

b. II only

c. III only

d. I, II, and III

Suppose that Ricardo and Anita attend different colleges. Ricardo's GPA is the same as the average GPA at his school. Anita's GPA is $0.70$ standard deviations above her school average. In complete sentences, explain why each of the following statements may be false.

a. Ricardo's actual GPA is lower than Anita's actual GPA.

b. Ricardo is not passing because his $z$ -score is zero.

c. Anita is in the $70^{th}$ percentile of students at her college.

How would you represent the area to the left of one in a probability statement?

Find the 80th percentile.

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