This graph has four distinct panels, each with a separate graphic. It is identical to Figure 3 with one exception. In each panel there is a smooth curve superimposed over the the vertical lines.
It may help to read the description for Figure 3.
Each of the smooth curves is a symmetrical Normal distribution curve with the highest point at die score = 3.5.
In the first panel, the horizontal axis is labeled "Single die score". The smooth curve extends below 1 and above 6 with the proportion of rolls about 0.05 at these points. It does not go near the tops of the vertical lines except at die score = 3 and = 5.
In the second panel, the horizontal axis is labeled "Mean of two dice scores". The smooth curve extends below 1 and above 6 with proportion of rolls about 0.02. It goes quite near to the tops of the vertical lines, although they are mostly a bit higher or lower than the curve, except at die score = 3.5.
In the third panel, the horizontal axis is labeled "Mean of four dice scores" and is numbered 1, 2, 3, 4, 5, 6. The smooth curve extends below 1 and above 6 but the proportion of rolls is very small, about 0.001. It goes very near to the tops of all the vertical lines.
In the fourth panel, the horizontal axis is labeled "Mean of six dice scores" and is numbered 1, 2, 3, 4, 5, 6. The smooth curve does not extend below 1 or above 6. It goes very, very near to the tops of all the vertical lines.
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This page maintained by Martin Bland.
Last updated: 20 January, 2020.