2.2.2.2 Z-score and Z-table

A value on the standard normal distribution is defined as a Standard Score or Z-score. This score represents the number of standard deviations an observation is from the mean, thus giving us a mechanism of how any normal distribution with different mean and standard deviation can be standardised with 0 mean and 1 standard deviation.

A positive Z-score indicates that the observation is above the mean, while a negative Z-score indicates that the observation is below the mean. Thus, through the Z-score, we can find out what percentile of data falls under the bell curve. Say, when we have a Z-score of 0 (Fig 2.15, chart a), the area under the bell curve is exactly half of the complete bell curve, hence it's 50% (area shaded in red).

Similarly, when we have a Z-score of 1 (Fig 2.15, chart b), the area under the bell curve is equal to the sum of the area within the Z-score of 0 (50%) and the area between the Z-score of 0 and Z-score of 1 (~34%), hence it's ~84% (Fig 2.15, area shaded in red).

For distribution of percentages, refer to…