If an entire population with μ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of ___ and a standard deviation of ___.

Mean of 0 and a standard deviation of 1.

Step-by-step explanation:

To transform the entire population into z-scores, one would need to normalize/standardize the scores.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

Given mathematically as

z = (x - μ)/σ

The normal distribution shows how much a set of data points spread out around the mean.

A z-score is basically expressing how many standard deviations away from the mean is a particular data point.

z-score for the mean = (μ - μ)/σ = (60 - 60)/8 = 0

And any variable that is one standard deviation away from the mean will have a z-score of 1.

For example, 68 is one standard deviation away from the mean.

z-score for 68

z = (x - μ)/σ = (68 - 60)/8 = 1.

It is evident that normal distribution, when converted to z-scores has a mean of 0 and a standard deviation of 1.

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