Q.6.52 - Elementary Statistics

Question

According to Table II, the area under the standard normal curve that lies to the left of $-2.08$ is $0.0188$. Without further consulting Table II, determine the area under the standard normal curve that lies to the right of $2.08$. Explain your reasoning.

Step-by-Step Solution

Answer

To the right of $-2.08$, the area under the standard normal curve is $0.0188.$

Step 1: Given Information

Given in the question that, 

The area under the standard normal curve to the left of $-2.08$ is $0.0188$.

We have to determine the area under the normal curve that lies to the right of $2.08$

Step 2: Explanation

The shape of a normal distribution is totally symmetrical. This means that the distribution curve can be split in half in the middle, yielding two equal halves. When one-half of the observations fall on each side of the curve, the curve takes on a symmetric shape.

The area under the normal curve to the right of $2.08$ will equal the area under the normal curve to the left of $-2.08$ due to the symmetry property of the normal curve.