A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10.When the distribution is standardized,what value will be obtained for a score of X = 58 from the original distribution?
A)X = 53
B)X = 55
C)X = 58
D)X = 61

Question

Quizplus · Accepted Answer

When standardizing a score, we use the formula: z = (X - µ) / σ.

For the original distribution with µ = 55 and σ = 6, we can calculate the z-score for X = 58 as:

z = (58 - 55) / 6 = 0.5

Now, to standardize the distribution to have µ = 50 and σ = 10, we use the formula:

X' = (z * σ) + µ

Substituting in the values, we get:

X' = (0.5 * 10) + 50 = 55

Therefore, a score of X = 58 in the original distribution will have a standardized score (z-score) of 0.5, and when standardized to the new distribution with µ = 50 and σ = 10, it will have a value of X' = 55.

The correct answer is B.

A Distribution with µ = 55 and σ = 6