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The Microprocessors, Which Are Used in Automobiles to Regulate Fuel

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The microprocessors, which are used in automobiles to regulate fuel consumption, are guaranteed against defects for 15,000 miles of use. Tests conducted in the laboratory under simulated driving conditions reveal that the distances driven before the microprocessors break down are exponentially distributed and that the average distance driven before the microprocessors fail is 80,000 miles. What is the probability that a microprocessor selected at random will fail during the warranty period? Please round the answer to the nearest hundredth.

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Definitions:

Short Run

A period during which at least one of a firm's inputs is fixed, limiting the firm's ability to adjust production in response to market changes.

Monopolistically Competitive

A market framework where numerous companies offer products that are alike but not exactly the same, providing room for a bit of market influence and variation in products.

Fixed Costs

Costs that do not vary with the level of output or sales, such as rent, salaries, or insurance premiums.

Profit-Minimizing

A situation in which a business aims to reduce its profits to minimize taxes or for strategic reasons, contrary to typical profit-maximizing objectives.

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