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Q.12

Expert-verified

Introductory Statistics

Found in: Page 385

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

What is the z-score of x= 9, if it is 1.5 standard deviations to the left of the mean?

The value of the $z -$ score will be - $1.5$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

z-score is the number of standard deviations from the mean value a data point is.

Step 2: Explanation

$z -$ score is the number of standard deviations from the mean value a data point is. If a z-score is equivalent to zero, the corresponding score is the mean value. If the z-score is equal to + $1$ , it is one standard deviation above the mean value and if the z-score is equal to - $1$ , it is one standard deviation below the mean value.

Step 3: Explanation

By using the z-score it can be measured by how many standard deviations ( $σ$ ), the value of x will lie below (left) or above (right) the mean ( $μ$ ) of the distribution. If the score is down the mean value, its corresponding Z score will be negative and if the score is above (right) the mean value, its corresponding z score will be positive

It is shown that the score, x= $9$ is $1.5$ standard deviations to the left of the mean.

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