DISTRIBUCIÓN GAMMA y GAMMA INCOMPLETA | Probabilidad y Estadística

DEVORESTAT9 4.4.067.
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.)
0.424
Correct: Your answer is correct.
seenKey 0.424
(b) What is the probability that a transistor will last at most 20 weeks? (Round your answer to three decimal places.)
0.567
Correct: Your answer is correct.
seenKey 0.567
Is the median of the lifetime distribution less than 20? Why or why not?
The median is less than
Correct: Your answer is correct.
seenKey less than 20, since
P(X ≤ mu tilde) = .5.
(c) What is the 99th percentile of the lifetime distribution? (Round your answer to the nearest whole number.)
50
Correct: Your answer is correct.
seenKey 50
(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 = 55
Correct: Your answer is correct.
seenKey 55 weeks
You may need to use the appropriate table in the Appendix of Tables to answer this question.