Cornell [ASQC Statistics Divis

Cornell [ASQC Statistics Division Newsletter, 14(1), 11–12, 1994] explained, in a lighthearted article, how a person could maximize the octane rating of the gas in his or her tank for a given cost, or conversely, minimize the cost for a given octane rating. Sample three service stations in your neighbourhood and for each service station determine the mixture of 87, 89, and 92 (or 93) octane that you should put in your car to maximize the octane rating for a $15 purchase. (Assume for the sake of the illustration that a mixture of different octanes won’t harm your engine.) Then determine how to obtain an octane rating of 88 for the lowest cost. Note that the problem involves weighted averages.

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