Poisson distribution (m = mean):
P(x) = e^(-m) m^x / x!
For (a):
Take (0.028)(8) = 0.224 (this is the mean). Find P(0) using the above formula.
For (b):
Take (0.028)(24) = 0.672 (this is the mean). Find P(0) using the above formula. Then subtract that value from 1. This will be your probability.
I hope this will help get you started.
The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.028 failure per hour.
(a) What is the probability that the instrument does not fail in an 8-hour shift?
(b) What is the probability of at least one failure in a 24-hour day?
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