A standard deviation is 2500 miles, so the range of 25,000 to 37,500 is 2 standard deviations below, and 3 standard deviation above the mean of 30,000. We aren't assuming anything about the distribution, but we sort of have to assume a normal distribution in order to answer. When you don't know anything about a distribution, this is generally what you do. The general rule for standard deviations is: +/- 1 SD: +/- 34% of population, for a total of 68% +/- 2 SD: Another 14% in either direction, for a total of 96% of population. +/- 3 SD, Another 2% in either direction, which pretty much captures the entire distribution (4 standard deviations from the mean is incredibly rare/unlikely) We have a range of +/- 1 SD, so we know that 68% percent o the tire 'population' is captured in the range. We also have one more standard deviation in both directions, so we add 28% to this number to get 96% of the population. We have a third standard deviation above the mean, so we add another 2% to arrive at 98% of the population.
