An industrial company provides health insurance to employees located at four different plants. Health insurance costs at each plant are independent of the costs at any other plant. Plant managers have calculated the following statistics:
| Plant | Average cost | Standard deviation |
|---|---|---|
| W | 2 | 1.0 |
| X | 2 | 1.0 |
| Y | 5 | 1.5 |
| Z | 7 | 2.0 |
Calculate the standard deviation of total company health insurance costs.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Solution: C
The variance of the total is the sum of the variances: 1 + 1 + 2.25 + 4 = 8.25. The standard deviation is the square root, 2.87.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.