Suppose you are tired of having to deal with the different scales used by these

Question

Suppose you are tired of having to deal with the different scales used by these four test... so you decide to convert them to a common scale that has a mean of 50 and a standard deviation of 10... Convert each of your clients scores to a score on this new scale....

four test.

Test 1.

score= 32

mean=36

standard deviation=8

Test 2.

client score=163

mean=140

standard deviation=25

Test 3

Score=172

Mean=150

Standard Deviation= 50

Test 4.

Score=62

mean=75

Standard deviation=10

Z scores for

test 1= -.5

test 2= .92

test 3= .44

test 4= -1.3

Explanation / Answer

The Z scores for each of the four tests are given, substitute them in the following Z score formula to obtain the raw score in the new scale.

Z=(X-mu)/sigma, where, X is raw score, mu is population mean, and sigma is population standard deviation.

Test 1.

-0.5=(X1-50)/10, X1=45

Test 2,

0.92=(X2-50)/10, X2=59.2

Test 3,

0.44=(X3-50)/10, X3=54.4

Test 4,

-1.3=(X4-50)/10, X4=37

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