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. If this model is correct, what is P(T ≤ 90)? (Round the final answer to four decimal places.)
Added by Jonathan W.
Step 1
Step 1: Recall the probability density function (PDF) of the Weibull distribution with parameters α and β is given by: f(t) = (α/β) * (t/β)^(α-1) * exp(-(t/β)^α) where t is the lifetime of the component. Show more…
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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.
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