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 24 weeks and standard deviation 12 weeks. (a) What is the probability that a transistor will last between 12 and 24 weeks? (Round your answer to three decimal places.) (b) What is the probability that a transistor will last at most 24 weeks? (Round your answer to three decimal places.) Is the median of the lifetime distribution less than 24? Why or why not? --Select-- 24, since P(X s) .5. The median is (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 t=

Answer 1

here mean =$\alpha$$\beta$ =24

and standard deviation =($\alpha$$\beta$²)^1/2=12

solving above:

$\alpha$=4

$\beta$=6

with above parameter:

a)

P(12<X<24) =0.424

b)

P(X<24) =0.567

c)

99th percentile =60

d)

99.5th percentile t =66