Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are

Question

Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.17 claim per month.

What is the probability that the dealership will wait at least 10 months until the next claim? (Round your answer to 4 decimal places.)

What is the probability that the dealership will wait at least a year? (Round your answer to 4 decimal places.)

What is the probability that the dealership will wait at least 2 years? (Round your answer to 4 decimal places.)

What is the probability that the dealership will wait at least 10 months but not more than 1 year? (Round your answer to 4 decimal places.)

Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.17 claim per month.

Explanation / Answer

? is the mean number of occurrences per time unit:

so ? = 0.17

F(x) = 1 - e-? x for x > 0

Part 1:

P(x > 10) = e-10 * 0.17

P(x > 10) = 0.1827

Part 2:

P(x > 12) = e-12 * 0.17

P(x > 12) = 0.1300

Part 3:

P(x > 24) = e-24 * 0.17

P(x > 24) = 0.0169

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