Suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime X (in weeks) has a gamma distribution with mean 32 weeks and standard deviation 16 weeks. (a) What is the probability that a transistor will last between 16 and 32 weeks? (Round your answer to three decimal places.) (b) What is the probability that a transistor will last at most 32 weeks? (Round your answer to three decimal places.) Is the median of the lifetime distribution less than 32? Why or why not? The median is 32, since P(X ≤ ) = .5. (c) What is the 99th percentile of the lifetime distribution? (Round your answer to the nearest whole number.) (d) Suppose the test will actually be terminated after t weeks. What value of t is such that only 0.5% of all transistors would still be operating at termination? (Round your answer to the nearest whole number.) t = weeks