Question

since the area under the normal curve within two standard deviations of the mean is 0.95, the area under the normal curve that corresponds to values greater than 2 standard deviations above the mean is 0.05.
○ true
○ false

Explanation:

Step1: Recall normal - curve property

The total area under the normal curve is 1. The area within two standard deviations of the mean is 0.95.

Step2: Calculate area outside two - standard - deviation range

The area outside two standard deviations of the mean is $1 - 0.95=0.05$. This area is split evenly between the two tails (values greater than 2 standard deviations above the mean and values less than 2 standard deviations below the mean).

Step3: Find area above 2 standard deviations

The area corresponding to values greater than 2 standard deviations above the mean is $\frac{0.05}{2}=0.025$, not 0.05.

Answer:

False