Question

How do I find the area under the normal distribution curve given the z-score or interval?

Answer 1

The total area under a normal curve = 1. Since the mean = 0, negative z-scores give the area `< 0.5` and positive z-scores yield areas `> 0.5 " and " < 1.0`

Explanation:

The total area under a normal curve = 1.

The mean = 0. Negative z-scores represent areas less than 0.5.

Positive z-scores represent areas above the mean that have areas `> 0.5 " and " < 1.0`

For example if the z-score `= -2.23`, from the z-table `0.0129` is the area under the normal distribution curve: `1.29 %`

If the z-score `= 1.64`, from the z-table `0.9495` is the the area under the normal distribution curve: `94.95 %`