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 0.21 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 0.21 claim per month.

Explanation / Answer

Mean rate of claims = 0.21 per month

(a) Here we have to wait at least 10 months for the next claim.

So, that means in the next 10 months there are no claims.

Expected number of claims in 10 months = 10 * 0.21 = 2.1

Pr(no claims in at least 10 months) = POISSON (x = 0 ; 2.1) = e-2.1 = 0.1225

(b) Now expected number of claims in 12 months = 12 * 0.21 = 2.52

Pr(no claims in atleast 12 months) = POISSON (X = 0 ; 2.52) = e-2.52 = 0.0805

(c) Now expected number of claims in 2 years = 24 * 0.21 = 5.04

Pr(no claims in atleast 24 months) = POISSON (X = 0 ; 5.04) = e-5.04= 0.0065

(d) Pr(wait at least 10 months but not more than 1 year) = Pr(It occur in between two months in between 10th month to 1 year) = 1 - Pr(it also doesn't occur in the twomonth)

Expected number of claims in 2 months = 2 * 0.21 = 0.42

Pr(it also doesn't occur in the twomonth) = POISSON( x = 0; 0.42) = e-0.42 = 0.6570

Pr(wait at least 10 months but not more than 1 year) = 1 -0.6570 = 0.3430

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