Question

The average police office completed a series of trainings with an average score of 35.6 and a standard deviation of 5.1 for his population of officers. The police chief decides he wants to standardize the scores for the yearly fitness test to make them easier to interpret. If this distribution is standardized so that the new distribution has a mean of 100 and standard deviation of 10, what would your old score of x = 30.4 be in the new, standardized distribution? (Hint: This is a two step problem).

A. 91.2

B. 90.2

C. 88.4

D. 89.8

Answer 1

An Z score can be used to convert a score on a particular scale to a standardized scale

Z = (X - mean)/standard deviation

Step 1:

Z score corresponding to x = 30.4 is calculated as

Z = (30.4 - 35.6)/5.1

Z = -1.02

Step 2

Use the Z score to find out the corresponding standardised score

-1.02 = (X₂ - 100)/10

X₂ = 89.8

Answer: D. 89.8