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A can company reports that the number of machine breakdown in an eight hour shift has a mean of 1.5. Find the probability that there will be (i) exactly 2 breakdowns; (ii) fewer than 2 breakdowns; (iii) no breakdowns in 3 consecutive shifts.

All Probabilities are taken from the Poisson Distribution Table.

(i) exactly 2 breakdowns
P(X = 2) = 0.2510
The probability there will be exactly 2 breakdowns is 0.2510 or 25.1%


(ii) fewer than 2 breakdowns
P(X = 1) + P(X = 0)
0.3347 + 0.2233 = 0.558
The probability that there will be fewer than 2 breakdowns is 0.558 or 55.8%


(iii) no breakdowns in 3 consecutive shifts.
P(X = 0) ^ 3
0.2233 ^ 3 = 0.0111
The probability that there will be no breakdowns in 3 consecutive shifts is 0.0111 or 1.11%


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