Introduction to Statistics

Question

The mean cost of individual health care insurance in one region of the country is $421 per month with a standard deviation of $78. Of those in the region who have individual health insurance, approximately what percentage spend between $343 and $499 on their insurance each month? Assume that individual health insurance costs in the region have a bell shaped distribution.

Answer 1

The top and bottom of the range are $78 above and below the mean (499 - 421 = 421 - 343 = 78). So they are 1 standard deviation to the left and right of the mean on the normal curve. This can be done by the simple empirical rule, which states that, in a normal distribution, 68% of the data is within 1 standard deviation of the mean. So about 68% spend between $343 and $499 on their insurance each month.