Question

Using z-scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution?
X = 43
It cannot be determined with the information given.
X = 40
X = 42

Answer 1

Answer:

X = 40

Step-by-step explanation:

Original mean (µ) = 37

Original standard deviation (σ) = 6

New mean (µ) = 50

New standard deviation (σ) = 10

The z-score of an individual who had a score of X=55 in the new distribution is given by:

$z=\frac{X-\mu}{\sigma}\\z=\frac{55-50}{10}\\z=0.5$

A z-score of 0.5, in the original distribution yields a score, X, of:

$0.5=\frac{X-37}{6}\\X=0.5*6 +37\\X=40$

This individual’s score in the original distribution is X = 40