Page "Tolerance interval" Paragraph 6

gives the following example: So consider once again a proverbial EPA mileage test scenario, in which several nominally identical autos of a particular model are tested to produce mileage figures.

If such data are processed to produce a 95 % confidence interval for the mean mileage of the model, it is, for example, possible to use it to project the mean or total gasoline consumption for the manufactured fleet of such autos over their first 5, 000 miles of use.

Such an interval, would however, not be of much help to a person renting one of these cars and wondering whether the ( full ) 10-gallon tank of gas will suffice to carry him the 350 miles to his destination.

For that job, a prediction interval would be much more useful.

( Consider the differing implications of being " 95 % sure " that as opposed to being " 95 % sure " that.

) But neither a confidence interval for nor a prediction interval for a single additional mileage is exactly what is needed by a design engineer charged with determining how large a gas tank the model really needs to guarantee that 99 % of the autos produced will have a 400-mile cruising range.

What the engineer really needs is a tolerance interval for a fraction of mileages of such autos.