The authors of the article "A Probabilistic Insulation Life Model for Combined Thermal Electrical Stresses" (IEEE Trans. on Elect, Insulation, 1985: 519-522) state that "the Wei bull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress." They propose the use of the distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose α = 2.5 and β = 200 (values suggested by data in the article).

a. What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300?

b. What is the probability that a specimen's lifetime is between 100 and 250?

c. What value is such that exactly 50% of all specimens have lifetimes exceeding that value?