Questions: The following is a graph of two normal distributions plotted on the same x-axis. Based on the graph above, which statement best describes the graph? The two distributions have equal means and standard deviations that differ by 3 units. The two distributions have equal means and equal standard deviations. The two distributions have means that differ by 3 units and different standard deviations. The two distributions have means that differ by 3 units and equal standard deviations.

Solution Steps

The means of normal distributions are represented by the x-coordinate of the peak of the curve. In the graph, the peaks of the two distributions have different x-coordinates, specifically, one at 8 and the other at 11. This implies the means are different. Since \(11 - 8 = 3\), the means differ by 3 units.

The standard deviation of a normal distribution influences the spread or width of the curve. A larger standard deviation leads to a wider, flatter curve, while a smaller standard deviation leads to a narrower, taller curve. In the provided graph, the two distributions have different widths. The distribution centered at 8 is narrower and taller than the distribution centered at 11, indicating different standard deviations.

The analysis shows that the two distributions have means that differ by 3 units and different standard deviations.

Final Answer