The normal distribution and Z scores

A special form of the normal probability distribution is the standard normal distribution, also known as the z - distribution. A z distribution has a mean of 0 and a standard deviation of 1. Often you can transform variables to z values. You can transform the values of a variable to z-scores by subtracting the mean, and dividing this by the standard deviation. If you perform this transformation on the values of a data set, your transformed data set will ave a mean of 0 and a standard deviation of 1. The formula to transform a value to a z score is the following:

$$Zi = \frac{xi - \bar{x}}{s_x}$$

The Z-score represents how many standard deviations from the mean a value lies.

Imagine we have a woman with a hair length of 38 centimers and the average hair length was 25 centimers and the standard deviation was 5 centimers. Calculate the Z value for this woman and store it in the variable z_value. Round z_value to one decimal.

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Exercise

The normal distribution and Z scores

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