Question

For a normally distributed variable, what is the relationship between the percentage of all possible observations that lie between 2 and 3 and the area under the associated normal curve between 2 and 3? What if the variable is only approximately normally distributed?

Short answer

The percentage of all percentage observation in a normally distributed variable that lies between 2 and 3 equals the area under the associated normal curve between 2 nad 3.

If the variable is approximately normally distributed, the percentage of all possible distributions that lies between 2 and 3 approximately equals the area under the same associated normal curve.

Step-by-step solution

Step 1. Given Information.

A normally distributed variable.

Step 2. The relationship.

The percentage of all percentage observation in a normally distributed variable that lies between 2 and 3 equals the area under the associated normal curve between 2 nad 3.

If the variable is approximately normally distributed, the percentage of all possible distributions that lies between 2 and 3 approximately equals the area under the same associated normal curve.