Question

consider the following normal curves, which of the following is true: the two curves have equal means. curve 1 has a larger mean. the two curves have equal medians. the two curves have equal standard deviations. curve 2 has a larger standard deviation. none of the above.

Explanation:

Step1: Recall normal - curve properties

In a normal distribution, the mean, median, and mode are equal and located at the center of the curve. The spread of the normal curve is determined by the standard deviation. A narrower curve has a smaller standard deviation and a wider curve has a larger standard deviation.

Step2: Analyze the given curves

Both Curve 1 and Curve 2 are centered at \(x = 0\). So, they have the same mean (and since for a normal distribution mean = median, they also have the same median). Curve 2 is wider than Curve 1. The standard - deviation of a normal distribution is related to the width of the curve. A wider curve implies a larger standard deviation.

Answer:

The two curves have equal means.
The two curves have equal medians.
Curve 2 has a larger standard deviation.