An auto manufacturer advertises that "90 percent of the cars we have ever made are still on the road." Assuming this is literally true, how can it be explained? What facts and/or statistics would you need to know to expose this misleading claim


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Oddman answered
It will be true if the average car lasts y years* and production growth is at least (10^(1/y) - 1)*100% each year. A 60% annual growth rate with a 5-year life will have this characteristic, as will a 40% annual growth rate and a 7-year life, or an 8% growth rate and a 30-year life.

The claim will be easily exposed if the number of the manufacturer's cars on the road is known, along with total production numbers. An inference can be made about the claim if one knows production numbers for several years, preferably along with numbers of cars in service or retired each year. (The vehicle licensing agency should have figures on the latter.) It is difficult to sustain the sort of growth rate required, given the usual life of a car.
* meaning that the total number of cars retired is less than the cumulative production y years ago.

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