Question

Which of the following statements is true about a normal density curve as ​increases?

a. the curve becomes less spread out.
b. there is no change in the spread of the curve.
c. the curve becomes more spread out.
d. there is not enough information to determine the effect on the spread of the curve.

Answer 1

As the standard deviation increases, a normal density curve will become more spread out, indicating that the data is more dispersed around the mean.

Step-by-step explanation:

When referring to a normal density curve the spread of the curve is directly related to the standard deviation. The question regarding how the curve changes as the standard deviation (σ) increases can be answered by understanding the properties of a normal distribution. As the standard deviation increases, the curve will become more spread out, which means that the data points are more dispersed around the mean. Therefore, the correct statement is c. the curve becomes more spread out.

The correct question is: Which of the following statements is true about a normal density curve as the standard deviation ​increases?