Question

In a normal distribution, a data value located 0.8 standard deviations below the mean has Standard Score: z =

In a normal distribution, a data value located 2.4 standard deviations above the mean has Standard Score: z =

In a normal distribution, the mean has Standard Score: z =

Answer 1

Using the normal distribution, it is found that the z-scores are:

1) z = -0.8

2) z = 2.4

3) z = 0

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

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean, either above the mean(positive z-score), or below(negative z-score).

Item 1:

0.8 standard deviations below the mean, hence z = -0.8.

Item 2:

2.4 standard deviations above the mean, hence z = 2.4.

Item 3:

The mean is 0 standard deviations from itself, hence z = 0.

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