The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6. What are the values of the mean and standard deviation after all test scores have been
Standardized by converting them to z-scores using $z = ( x - \mu ) / \sigma$ ?
A) The mean is 10 and the standard deviation is 100.
B) The mean is 0 and the standard deviation is 1.
C) The mean is 100 and the standard deviation is 10.
D) The mean is 1 and the standard deviation is 0.

Question

Quizplus · Accepted Answer

Standardizing by z-scores always results in a normal distribution with a mean of 0 and a standard deviation of 1. When we convert all test scores to z-scores using the given formula, we shift the original mean and scale the original standard deviation to become the new mean of 0 and the new standard deviation of 1. Therefore, the correct choice is B.

The Distribution of Certain Test Scores Is a Nonstandard Normal z=(x−μ)/σz = ( x - \mu ) / \sigmaz=(x−μ)/σ

The Distribution of Certain Test Scores Is a Nonstandard Normal $z = ( x - \mu ) / \sigma$