A population with μ = 45 and s = 8 is standardized to create a new distribution with μ = 100 and s = 20.In this transformation,a score of X = 41 from the original distribution will be transformed into a score of X = 110.

Question

Quizplus · Accepted Answer

If we use the formula for transforming scores into standard scores:
z = (X - μ)/s
We can plug in the values for the original distribution (μ = 45, s = 8) and the given score of X = 41:
z = (41 - 45)/8 = -0.5
Then, using the formula for transforming standard scores back into raw scores:
X = z*s + μ
We can plug in the values for the new distribution (μ = 100, s = 20) and the calculated standard score:
X = (-0.5)*20 + 100 = 90
Therefore, a score of X = 41 from the original distribution would be transformed into a score of X = 90 in the new distribution, not X = 110.

A Population with μ = 45 and S = 8