Question

In a food processing and packaging plant, there are, on average, two packaging machine breakdowns per week.
(a) Calculate the probability that there are no more than two machine breakdowns in a
given week.
(b) What is the probability that there are no machine breakdowns in a given week?
(c) In a random sample 26 machines, what is the probability that there are no machine
break downs in at least one of them in a given week?

Answer 1

The Poisson distribution applies to part (a):
\[\large P(X=x)=\frac{e^{-\lambda} \lambda^{x}}{x!}\]
where lambda is the average number of machine breakdowns per week. In this case:
\[\large \lambda=2\]
You need to calculate P(X = 0), P(X = 1) and P(X = 2). Then sum these 3 values of probability to find the probability that there are no more than two machine breakdowns in a week.