The microprocessors manufactured by United Motor Works, which are used in automo

Question

The microprocessors manufactured by United Motor Works, which are used in automobiles to regulate fuel consumption, are guaranteed against defects for 16,000 mi of use. Tests conducted in the laboratory under simulated driving conditions reveal that the distances driven in miles before the microprocessors break down are exponentially distributed and that the average distance driven before the microprocessor fails is 100,000 mi. What is the probability that a microprocessor selected at random will fail during the warranty period? (Round your answer to 3 decimal places.)

Explanation / Answer

Xi~iid exponential with mean 100,000

P(Xi<16000)

= F(16,000)

=1-e^(-16000/100000)

=1-e^-0.16

=1-0.852

=0.148

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