the graph shows the distribution of hand lengths, in centimeters, of the members of an orchestra. what is…

Explanation:

Step1: Recall variance - standard deviation relationship

For a normal - distributed data (the graph appears to be a normal distribution), if we assume that approximately 95% of the data lies within 2 standard - deviations of the mean in a normal distribution. Looking at the graph, we can estimate that the range within which about 95% of the data lies is from approximately 17 to 23. The mean is around 20. The range of this interval is (23 - 17=6). Since this range is approximately (4\sigma) (where (\sigma) is the standard deviation), then (\sigma=\frac{6}{4} = 1.5).

Step2: Calculate the variance

The variance (\sigma^{2}) is related to the standard deviation (\sigma) by the formula (\sigma^{2}=\sigma\times\sigma). If (\sigma = 2) (a common - sense estimate from the graph, as the range from the mean to a point where the curve starts to decline significantly can be used to estimate standard deviation. A more accurate way: assume the range of the middle 95% of data for a normal distribution is (4\sigma). If we assume the range of the middle part of the curve is from 17 to 23, range (=6), (\sigma=\frac{6}{4}=1.5\approx2)), then the variance (\sigma^{2}=4).

Answer:

4