Question

A population with μ = 41 and σ = 4 is standardized to create a new distribution with μ =50 and σ = 10. In this transformation, a score of X = 39 from the original distribution will be transformed into a score of X = 55. True or False?

Answer 1

Solution:
Given in the question
= 41
= 4
Score X = 39,
Z-score for X=39 can be calculated as
Z-score = (X-)/ = (39-41)/4 = -2/4 = -0.5
X=39, Score is 0.5 standard deviation below from the mean.

New distribution with = 50
= 10
Z-score for X = 55 can be calculated as
Z-score = (55 -50)/10 = 0.5
That means the X = 55 score is 0.5 standard deviation above the mean.
So we can say that a score from the original distribution will not be transformed into a score of X=55 as Z-scores are different for both the distribution.
So this statement is False that a score of X = 39 from the original distribution will be transformed into a score of X = 55.