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 28 weeks and standard deviation 14 weeks. (a) What is the probability that a transistor will last between 14 and 28 weeks? (Round your answer to three decimal places.) :I (b) What is the probability that a transistor will last at most 28 weeks? (Round your answer to three decimal places.) :I Is the median of the lifetime distribution less than 28? Why or why not? The median is 28, since P(X 5 I1) = .5. (c) What is the 99th percentile of the lifetime distribution? (Round your answer to the nearest whole number.) :I (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.)