Suppose that when a transistor(晶体管) of a certain type is subjected to an accelerated life test, the lifetime $X$ (in weeks) has a gamma distribution with mean $24$ weeks and standard deviation $12$ weeks.

• (a) What is the probability that a transistor will last between $12$ and $24$ weeks?
• (b) What is the probability that a transistor will last at most $24$ weeks? Is the median of the lifetime distribution less than $24$? Why or why not?
• (c) What is the $99$th percentile of the lifetime distribution?
• (d) Suppose the test will actually be terminated after $t$ weeks. What value of $t$ is such that only $.5\%$ of all transistors would still be operating at termination?