Question

Asked Jul 18, 2019

The lifetime mileage of a car can be modeled as a Weibull variable with parameter λ = 1 per 150000 miles and parameter a=1.25.

a) What is the probability that a car will last between 100000 and 150000 miles?

b) A dealer sold 10 cars on a day with a guarantee that any car lasting less than 100000

miles will be replaced by another car with a 30% discount. What is the probability

that the dealer has to provide the discount on 2 or fewer of these cars?

Step 1

It is given that the lifetime mileage of a car can be modelled as a Weibull variable with parameter λ=1 per150,000 miles and parameter a=1.25.

The cdf of a Weibull distribution with λ = 1 per 150,000 miles and a = 1.25 is given as follows:

Step 2

**a.**

Define the random variable *X* as the lasting time of a car.

The probability that a car will last between 100,000 and 150,000 miles is obtained as shown below:

Step 3

**b.**

It is given that a dealer sold 10 cars on a day with a guarantee that any car lasting less than 1000,000 miles will be replaced by anothe...

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