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Question 8 In an industrial engineering article, the authors suggest using a Weibull distribution to model the duration of a bake step in the manufacture of a semiconductor. Let T represent the duration in hours of the bake step for a randomly chosen lot. Suppose T has Weibull distribution with scale parameter 8 and shape parameter 1.29. (9 pts.) Part a) What are the parameters of T? Is this a valid probability density function? (1 pts.) Part b) What is the probability that the bake step takes longer than 7 hours? Illustrate the desired probability on the pdf plot. Calculate the same probability using standard uniform transformation. (3 pts.) Part c) # What is the probability that the bake step takes between 3 and 7 hours? Illustrate the desired probability on the pdf plot. Calculate the same probability using standard uniform transformation. (3 pts.) Part d) # Calculate the mean time to failure, variance and standard deviation of T. (2 pts.)