Question

Suppose that taxis in New York are driven an average of 60,000 miles per year with a standard deviation of 11,000 miles. Assume that the mileage driven for a year is normally distributed.
How many miles will the middle 95% of taxis have driven in one year?

Answer 1

Let n be the number of taxis in NY. The average distance travelled is 60,000 miles, therefore the middle 95% will have the same average as the population, the reason being the mileage is symmetrically distributed about the mean Therefore the total number of miles in one year for the middle 95% is 60,000 * 0.95 * n
The range of miles driven by the middle 95% can be found from the empirical rule that says: For a normal distribution, approximately 95% of the data points lie within the range plus and minus 2 standard deviations of the population mean. In this case the range is (60,000-22,000) to (60,000 + 22,000)