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 100 and the standard deviation is 10 .
B) The mean is 0 and the standard deviation is 1 .
C) The mean is 10 and the standard deviation is 100 .
D) The mean is 1 and the standard deviation is 0 .

Question

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 100 and the standard deviation is 10 .
B) The mean is 0 and the standard deviation is  1 . 
C) The mean is 10 and the standard deviation is 100 .
D) The mean is 1 and the standard deviation is  0 .

Quizplus · Accepted Answer

Standardizing a distribution using $z = (x - \mu) / \sigma$ transforms it into a standard normal distribution with a mean of 0 and a standard deviation of 1.

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

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