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 20 weeks and standard deviation 10 weeks. (a) What is the probability that a transistor will last between 10 and 20 weeks? (Round your answer to three decimal places.) E {b} What is the probability that a transistor will last at most 20 weeks? (Round your answer to three decimal places.) E Is the median of the lifetime distribution less than 20? Why or why not? The median is 20. since P{X 5 E) = .5. (c) What is the 99th percentile of the lifetime distribution? (Round your answer to the nearest whole number.) E {d} Suppose the test will actually be terminated after 1* 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.) You may need to use the appropriate table in the Appendix ofTables to answer this