Question

What happens to the graph of the normal curve as the mean​ increases?

A. The graph of the normal curve compresses and becomes steeper.
B. The graph of the normal curve slides right.
C. The graph of the normal curve flattens out and becomes wider.
D. The graph of the normal curve slides left.
E. Nothing happens to the graph of the normal curve.

Answer 1

As the mean of a normal distribution increases, the graph of the normal curve slides to the right. Therefore, option B is the correct answer.

This is because the mean of a normal distribution represents the center of the distribution. As the mean increases, the center of the distribution shifts to the right. This means that the values on the right side of the distribution become more probable, and the values on the left side become less probable. This causes the normal curve to slide to the right.

It's worth noting that changing the mean does not affect the shape or spread of the normal curve. The shape and spread of the curve are determined by the standard deviation. If the standard deviation is large, the curve will be wider and flatter, and if the standard deviation is small, the curve will be narrower and taller.

Answer 2

The graph of the normal curve slides to the right as the mean increases, while its shape remains unchanged if the standard deviation is constant.

Step-by-step explanation:

When considering what happens to the graph of the normal curve as the mean increases, it is important to understand that the mean is the center of the distribution. As the mean (μ) increases or decreases, the entire graph of the normal distribution will slide along the x-axis. The correct answer to the question is that the graph of the normal curve slides right as the mean increases, thus making option B the correct choice. It is important to note that increasing the mean does not alter the shape of the curve, provided the standard deviation remains constant; it does not become steeper or flatter, nor does it compress. The curve's symmetry about the mean is maintained.