An actuarial firm is conducting an analysis to model health insurance costs for two companies. One of the many factors they are using in the model is the ages
of employees of the two companies. The firm has collected data on the ages (in years) of 62 employees of each company. The histograms below show the
distributions of the two data sets. Each histogram shows age (in years) on the horizontal axis and the number of employees on the vertical axis. The means and
standard deviations for the data sets are also given.
Company A
Company B
20
15-
10+
5-
19.5 24.5 295 345 39.5 445 495 545 59.5
Company A mean: 39.26 years
Company A standard deviation: 6.25 years
20+
15-
10+
54
0
19.5 24.5 295 345 39.5 445 495 545 595
Company B mean: 30.79 years
Company B standard deviation: 8.99 years
The firm wants to use the Empirical Rule to make some approximations about both data sets. Unfortunately, it is appropriate to use the Empirical Rule on only
one of them!
Answer the parts below to help the actuarial firm with their approximations.
(a) Identify the data set for which it is appropriate to use the Empirical Rule.
It is appropriate to use the Empirical Rule for the Company A data set.
For the data set identified in part (a), use the Empirical Rule to make the following approximations.
(b) The percentage of ages between 20.51 years and 58.01 years is approximately 95%
(c) Approximately 95% of the ages are between years and years.