Question

draw two normal curves that have the same mean but different standard deviations. describe the similarities and differences. compare the two curves. the two curves will have of symmetry. the curve with the larger standard deviation will be spread out than the curve with the smaller standard deviation.

Explanation:

• For normal curves, the line of symmetry is \(x = \mu\) (where \(\mu\) is the mean). Since the two curves have the same mean, they have the same line of symmetry.
• The standard deviation \(\sigma\) measures the spread of the data. A larger \(\sigma\) means the data is more spread out, so the normal curve with a larger standard deviation is more spread out.

Answer:

The two curves will have the same line of symmetry. The curve with the larger standard deviation will be more spread out than the curve with the smaller standard deviation.