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 0.10 claim per month.

What is the probability that the dealership will wait at least 9 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 9 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 0.10 claim per month.

Explanation / Answer

lambda = 0.1
a)
P(X > 9) = 1 - e^-lambda * x
= 1 - e^ ( -0.1 *6)
= 0.4066

b)
P(X > 12) = 1 - e^-lambda * x
= 1 - e^ ( -0.1 *12)
= 0.3012

c)
P(X > 24) = 1 - e^-lambda * x
= 1 - e^ ( -0.1 *24)
= 0.0907

d)
P(9 < x < 12) = ( 1 - e^ (-0.1 *12)) - ( 1 - e^ (-0.1 *9))
= 0.4066 - 0.3012 = 0.1054

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