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 0.1 claim per month. (a) What is the probability that the dealership will wait at least 6 months until the next claim? (Round your answer to 4 decimal places.) Probability (b) What is the probability that the dealership will wait at least a year? (Round your answer to 4 decimal places.) Probability (c) What is the probability that the dealership will wait at least 2 years? (Round your answer to 4 decimal places.) Probability (d) What is the probability that the dealership will wait at least 6 months but not more than 1 year? (Round your answer to 4 decimal places.) Probability

a) Probability: 0.5488

b) Probability: 0.3012

c) Probability: 0.0907

d) Probability: 0.2476

Step-by-step explanation:

a) We can model this as a Poisson process, with parameter r=0.1.

We have to calculate the probability that no claim is made in 6 months.

The probability that the dealership will wait at least 6 months until the next claim is 0.5488.

b) In this case, t=12 months.

c) In this case, t=24 months

d) In this case, we have to multiply the probability that there is no claim in the first 6 months (k=0, t=6) and the probability that there is more than one claim in the next 6 months (k>0, t=6).

As the Poisson process is memoryless, the probabilitiies are independent of past events and can be calculated that way.

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step-by-step explanation: