In the context of a normal distribution, what does a flatter (wider) distribution curve indicate about the standard deviation?

• A. The sample size is larger, which makes the curve flatter regardless of spread.
• B. The standard deviation is larger, meaning the data are more spread out around the mean.
• C. The mean is larger, shifting the entire curve to the right without changing spread.
• D. The standard deviation is smaller, meaning the data are more tightly clustered around the mean.

Answer: (B)

Verified step by step guidance

1. Recall that in a normal distribution, the shape of the curve is determined by two parameters: the mean (\( \mu \)) and the standard deviation (\( \sigma \)).
2. Understand that the mean (\( \mu \)) determines the center or the peak location of the curve, but it does not affect the spread or width of the curve.
3. Recognize that the standard deviation (\( \sigma \)) controls the spread of the data around the mean. A larger standard deviation means data points are more spread out, resulting in a wider and flatter curve.
4. Conversely, a smaller standard deviation means data points are closer to the mean, producing a narrower and taller curve.
5. Therefore, a flatter (wider) normal distribution curve indicates a larger standard deviation, reflecting greater variability in the data.