The maintenance department in a factory claims that the number of breakdowns of
ID: 3336108 • Letter: T
Question
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 4 breakdowns every 368 hours. Let x denote the time (in hours) between successive breakdowns.
Assuming that the maintenance department's claim is true, find the probability that the time between successive breakdowns is at most 4 hours. (Round your answer to 4 decimal places.)
Assuming that the maintenance department's claim is true, find the probability that the time between successive breakdowns is between 95 and 278 hours. (Round your answer to 4 decimal places.)
Suppose that the machine breaks down 4 hours after its most recent breakdown. Based on your answer to part d, do you believe the maintenance department's claim? (Round your answer to 4 decimal places.)
(a) Find and x. (Write the fraction in reduced form.)Explanation / Answer
a) x = = 368/4 =92
b) f(x) = (1/92) e-(x/92) for x .0
d)P(X<4) =1-e-4/92 =0.0425
e) P(95<X<278)=(1-e-278/92 )-(1-e-95/92 ) =0.3074
f)
Probably not ; the probability of this result is quite smalllar if the claim is true.
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