   Chapter 5, Problem 4P Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912

Solutions

Chapter
Section Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

For a population with μ = 60 and σ = 12 Find the a-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.)    X = 75 X = 48 X = 84 X = 54 X = 78 X = 51 Find the score (X value) that corresponds to each of the following z-scores. (Again, you should not need a formula or any serious calculations.)    z = 1.00 z = 0.25 z = 1.50 z = − 0.50 z = − 1.25 z = − 2.50

To determine
1. For given mean and standard deviation (SD) find Z score for given X values.
2. To find corresponding X value for given Z scores.
Explanation

Given:

a) Populations with mean=60 and standard deviation =12 and some given X values.

b) Populations with mean=60 and standard deviation =12 and some given Z scores.

Key Point:

a) In order to calculate Z scores using the given mean, SD (standard deviation) and X values we have to use the formula for Z scores which is

Z=( Xmean )/sd

b) In order to calculate X scores using the given mean, SD and Z values we have to use the formula:

X=Z×sd+mean

Calculation:

a) mean =60, sd=12

Let's calculate Z for X=75 (other values are calculated in similar fashion and

Presented in Table (a)

Z=( Xmean )/sd=( 7560 )/12=1.25 For X=48,Z=( 4860 )/12=1 X=84,Z=( 8460 )/12=2 X=54,Z=( 5460 )/12=

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