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?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
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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?
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