Questions: Based on the graph above, which statement best describes the graph? Answer O The two distributions have equal means and equal standard deviations. O The two distributions have equal means and standard deviations that differ by 4 units. O The two distributions have means that differ by 4 units and different standard deviations. O The two distributions have means that differ by 4 units and equal standard deviations. © 2024 Hawkes Learning

Solution Steps

The means of normal distributions are represented by the x-value at the peak. Both distributions have a peak at x=9. Therefore, they have equal means.

The standard deviation of a normal distribution relates to the spread or width of its curve. A smaller standard deviation corresponds to a narrower curve. In the graph, the dotted line distribution is narrower than the solid line distribution, implying that they have different standard deviations.

Since the distributions have equal means and different standard deviations, the correct option is "The two distributions have equal means and different standard deviations".

Final Answer: The two distributions have equal means and different standard deviations.