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.)


(b) What is the probability that a transistor will last at most 28 weeks? (Round your answer to three decimal places.)


Is the median of the lifetime distribution less than 28? Why or why not?The median is ---Select--- less than equal to greater than 28, 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