Given four normal curves with the same mean ($\mu$) but different spreads, which one of the following curves has the largest standard deviation ($\sigma$)?

• A. The curve that is the most spread out and flattest
• B. The curve that is the tallest and most narrow
• C. The curve that is skewed to the right
• D. The curve that is symmetric but has the smallest spread

Answer: (A)

Verified step by step guidance

1. Recall that the standard deviation of a normal distribution measures the spread or dispersion of the data around the mean. A larger standard deviation means the data is more spread out.
2. Understand the shape of a normal curve: it is symmetric and bell-shaped. When the standard deviation increases, the curve becomes wider and flatter because the data is more spread out.
3. Conversely, when the standard deviation decreases, the curve becomes narrower and taller because the data is more concentrated around the mean.
4. Since all curves have the same mean, the difference in their shapes is due to their standard deviations. The curve that is the most spread out and flattest corresponds to the largest standard deviation.
5. Therefore, among the given options, the curve described as the most spread out and flattest has the largest standard deviation.