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

Answer:

4

Explanation:

Step1: Recall variance property of normal - like graph

For a normal - like distribution, if we assume a "standard" spread pattern. In a normal distribution, approximately 68% of the data lies within 1 standard deviation ($\sigma$) of the mean. Looking at the graph, if we assume the mean is around 19 and the data from 17 to 21 (a range of 4) contains about 68% of the data. So, the standard deviation $\sigma\approx2$.

Step2: Calculate variance

The variance $\sigma^{2}$ is related to the standard deviation by the formula $\sigma^{2}=\sigma\times\sigma$. Since $\sigma = 2$, then $\sigma^{2}=2\times2 = 4$.