In a factory, producing parts for an automobile, the parts manufactured on the shop floor are required to go through three quality checks, each conducted after a specific part of the processing on the raw material is completed. Only parts that are not rejected at one stage are put through the subsequent stages of production and testing. If average rejection rates at these testing machines during a month are 10\%, 5\% and 2\% respectively, then what is the effective rejection rate for the whole plant?
(a)15.20\%
(b)16.21\%
(c)16.48\%
(d)17\%
Answer
Answer (as printed): B
Explanation
Let the number of parts before the quality checks be 100. Then, number of parts passed after quality checks$$\begin{aligned} & =(100-2) \% \text { of }(100-5) \% \text { of }(100-10) \% \text { of } 100 \\ & =98 \% \text { of } 95 \% \text { of } 90 \% \text { of } 100 \\ & =\left(\frac{98}{100} \times \frac{95}{100} \times \frac{90}{100} \times 100\right)=\left(\frac{8379}{100}\right)=83.79 . \end{aligned}$$ ∴ Effective rejection rate $=(100-83.79) \%=16.21 \%$.
Explanation as extracted from the printed page; notation may be imperfect.