What does increasing the standard deviation in a normal distribution do?

What does increasing the standard deviation in a normal distribution do?

• A. Flattens and spreads out the curve
• B. Points the curve more sharply
• C. Does not affect the curve
• D. Increases the mean

Answer: (A)

Increasing the standard deviation in a normal distribution results in a flatter and more spread-out curve. The standard deviation measures the amount of variability or dispersion in a set of data points. When the standard deviation increases, it indicates that the data points are more spread out from the mean. In practical terms, as you increase the standard deviation, the tails of the distribution become longer and the peak of the curve becomes lower. This reflects a greater likelihood of extreme values occurring, as the data is less concentrated around the mean. The result is a bell-shaped curve that is wider and less steep, which visually represents the increased variability within the data set. Conversely, a decrease in standard deviation would result in a curve that is taller and narrower, indicating that more data points cluster closely around the mean. Therefore, the correct choice illustrates the relationship between standard deviation and the shape of the normal distribution effectively.

Increasing the standard deviation in a normal distribution results in a flatter and more spread-out curve. The standard deviation measures the amount of variability or dispersion in a set of data points. When the standard deviation increases, it indicates that the data points are more spread out from the mean.

In practical terms, as you increase the standard deviation, the tails of the distribution become longer and the peak of the curve becomes lower. This reflects a greater likelihood of extreme values occurring, as the data is less concentrated around the mean. The result is a bell-shaped curve that is wider and less steep, which visually represents the increased variability within the data set.

Conversely, a decrease in standard deviation would result in a curve that is taller and narrower, indicating that more data points cluster closely around the mean. Therefore, the correct choice illustrates the relationship between standard deviation and the shape of the normal distribution effectively.