Statistics for Business: Decision Making and Analysis, 3rd Edition

... expected cost for labor, for the addition, is around $12,000. This figure is not guaranteed, and the owner should not be too surprised if costs are higher (or lower) by $2,000. (If we believe that the distribution of costs is bell shaped, then the Empirical Rule implies that there’s about a 2/3 chance that costs are within $2,000 of the mean.)

Best Practices

• Consider the possibility of dependence. Independent random variables are simpler to think about, but unrealistic unless we’re rolling dice or tossing coins. Ignoring dependence can produce poor estimates of variation. Make sure that it makes sense for random variables to be independent before you treat them as independent.

• Only add variances for random variables that are uncorrelated.