Many companies face the challenge of demonstrating that their products satisfy some type of quality, reliability, safety or environmental criteria. In these situations, there's no single correct answer, but a trade-off between two competing objectives such as maximizing safety while controlling costs. Veeder-Root, a manufacturer that supplies gas stations with submersible pumps and pressurized line-leak detectors, must demonstrate to the California Air Resources Board (CARB) that its new diagnostic system for monitoring the gas station vapor-recovery systems complies with CARB regulations: The diagnostic system must catch at least 95 percent of all true failures with no more than 1 percent false alarms.

The primary tools needed to make decisions regarding quality and safety on the one hand, and the costs involved on the other, include basic probability, statistics and algebra (including the binomial theorem). This task also requires the ability to conduct research, give and follow directions, summarize technical text, and — for its written report and oral presentation to the regulatory board — develop ideas systematically and make effective arguments.

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