W. Nelson (Journal of Quality Technology, July 1985) suggests that the Weibull distribution usually provides a better representation for the life length of a product than the exponential distribution. Nelson used a Weibull distribution with α = 1.5 and β = 110 to model the life length Y of a roller bearing (in thousands of hours).

a. Find the probability that a roller bearing of this type will have a service life of less than 12.2 thousand hours.

b. Recall that a Weibull distribution with α = 1 is an exponential distribution. Nelson claims that very few products have an exponential life distribution, although such a distribution is commonly applied. Calculate the probability from part a using the exponential distribution. Compare your answer to that obtained in part a.