Question

Without consulting Table II, explain why the area under the standard normal curve that lies to the right of $0$ is $0.5$.

Short answer

The area under the standard normal curve to the right of $0$is $0.5$, as seen in the graph below:

Step-by-step solution

Given Information

The area to the right of $0$ under the standard normal curve is $0.5$.

Explanation

The histogram of the distribution is substantially bell-shaped when the variable is approximately distributed normally, as seen below:

The area beneath the standard normal curve is $1$and the curve is symmetric around $0$.

As a result, the area under the standard normal curve to the right of $0$is $0.5$, as shown in the diagram below: