The microprocessors, which are used in automobiles to regulate fuel consumption, are guaranteed against defects for 20,000 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 120,000 miles. What is the probability that a microprocessor selected at random will fail during the warranty period?
A) 0.15
B) 0.12
C) 0.36
D) 0.63
E) 0.85

Question

Quizplus · Accepted Answer

The probability that a microprocessor will fail during the warranty period is given by the cumulative distribution function of the exponential distribution:P(X < 20,000) = 1 - e^(-20,000/120,000) = 0.15

The Microprocessors, Which Are Used in Automobiles to Regulate Fuel