   Chapter 5, Problem 6P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

For a population with a mean of μ = 100 and a standard deviation of σ = 20,a. Find the z-score for each of the following X values.X = 108X = 115X = 130X = 90X = 88X = 95b. Find the score (X value) that corresponds to each of the following c-scores.z=– 0.40z= –0.50z= 1.80z = 0.75z = 1-50z = -1.25

(a)

To determine

To find: The z-score corresponding to X.

Explanation

Given info:

The population has mean μ=100 and standard deviation σ=20.

Calculation:

The z-score is used to transform any distribution in to standardized distribution with a predetermined mean and a predetermined standard deviation.

The formula for calculating z-score is,

z=Xμσ

Substitute μ=100 and σ=20. in the above equation.

The z-score corresponding to X=108 is,

z=Xμσ=10810020=0.4

The z-score corresponding to X=115 is,

z=Xμσ=11510020=0.75

The z-score corresponding to X=130 is,

z=XMs=13010020=1

(b)

To determine

To Find: The X value corresponding to z-scores.

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