What effect does decreasing standard deviation have in a normal distribution?

What effect does decreasing standard deviation have in a normal distribution?

• A. The density becomes flatter
• B. The curve becomes more pointed
• C. The central line shifts up
• D. The data becomes more spread out

Answer: (B)

Decreasing the standard deviation in a normal distribution results in a curve that becomes more pointed or peaked around the mean. This is because the standard deviation is a measure of the spread of data points around the mean; when the standard deviation is smaller, the data points cluster more closely around the mean. As a result, the tails of the distribution become narrower, leading to a sharper peak in the middle. In contrast, a larger standard deviation would result in a flatter curve, as data points would be more spread out, which is why the other options don't align with the characteristics of a normal distribution when the standard deviation is decreased. The central line of the distribution remains unchanged in height regardless of the standard deviation, and the data does not become more spread out; instead, it becomes more concentrated around the mean. Thus, the key change is the height and sharpness of the peak, confirming that the correct choice reflects the effect of reduced standard deviation.

Decreasing the standard deviation in a normal distribution results in a curve that becomes more pointed or peaked around the mean. This is because the standard deviation is a measure of the spread of data points around the mean; when the standard deviation is smaller, the data points cluster more closely around the mean. As a result, the tails of the distribution become narrower, leading to a sharper peak in the middle.

In contrast, a larger standard deviation would result in a flatter curve, as data points would be more spread out, which is why the other options don't align with the characteristics of a normal distribution when the standard deviation is decreased. The central line of the distribution remains unchanged in height regardless of the standard deviation, and the data does not become more spread out; instead, it becomes more concentrated around the mean. Thus, the key change is the height and sharpness of the peak, confirming that the correct choice reflects the effect of reduced standard deviation.