Question

Quality control testing has shown that 5% of the articles produced by a machine are defective. Find the probability that out of 30 articles produced, the following will occur:

(a) exactly 3 will be defective.
(b) all of the articles produced are good.
(c) more than 2 will be defective.
(d) What is the expected number of defective articles?

Answer 1

(a) the solution can be found by using the binomial distribution:
\[P(3\ out\ of\ 30\ are\ defective)=\left(\begin{matrix}30 \\ 3\end{matrix}\right)\times(0.05)^{3}\times(0.95)^{27}\]
\[=4060\times0.000125\times0.25=you\ can\ calculate\]