A set of test scores are normally distributed. The mean is 100 and the standard deviation is 20. These scores are converted to standardized units. What are z-scores of the mean and median

In a normal distribution, the mean and median values will be the same, in this case, 100. Therefore, both the mean and median will have the same score.

The z-score is given by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = 100:

[tex]z=\frac{100-100}{20}\\ z=0[/tex]

The z-scores of both the mean and the median are zero.

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joaobezerra joaobezerra · Answer 2 · 2021-10-28T12:28:33+02:00

Using the z-score concept, it is found that the z-scores of the mean and of the median are of 0.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

Mean of 100, standard deviation of 20, thus [tex]\mu = 100, \sigma = 20[/tex].
In the normal distribution, the mean and the median are the same, thus the z-score is Z when X = 100.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 100}{20}[/tex]

[tex]Z = 0[/tex]

The z-scores of the mean and of the median are of 0.

A similar problem is given at https://brainly.com/question/14785325