Question

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.) (b) What is the probability that a transistor will last at most 20 weeks? (Round your answer to three decimal places.) Is the median of the lifetime distribution less than 20? Why or why not? The median is ---Select 20, since P(X p) = .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.) weeks

Answer 1

here mean $\alpha$$\beta$ =20

and variance =$\alpha$$\beta$² =10² =100

solving above:

$\alpha$ =4 and $\beta$=5

a)

P(10 <X <20 )=0.424

b)

P(X<20) =0.567

c)

the median is less than 0.5

c)

99th percentile =50

d)

t =99.5th percentile =55