Someone suggests that the lifetime T (in days) of a certain component can be modeled with the Weibull distribution with parameters α = 3 and β = 0.01.

a. If this model is correct, what is P(T ≤ 1)?

b. Based on the answer to part (a), if the model is correct, would one day be an unusually short lifetime? Explain.

c. If you observed a component that lasted one day, would you find this model to be plausible? Explain.

d. If this model is correct, what is P(T ≤ 90)?

e. Based on the answer to part (d), if the model is correct, would 90 days be an unusually short lifetime? An unusually long lifetime? Explain.

f. If you observed a component that lasted 90 days, would you find this model to be plausible? Explain.