Answer to Question #233182 in Statistics and Probability for Bless

Question

A production process produces bottles of MacLean’s mouth wash from GlaxoSmithKline Group of Companies. On average, 20% of all bottles produced are defective. Each bottle is inspected before being dispatched. Items that pass inspection are dispatched and those not classified good are scrapped. Statistics from the quality assurance division reveals that a quality inspector’s probability of misclassifying a single bottle is 0.1.

           (i)       What proportion of the bottles will be classified good?

           (ii)      What is the quality of dispatched mouth wash  what percentage of mouth

                       washes dispatched are good?

Answer 1

(i) Proportion of bottles classified as good is 0.8 or $\frac{4}{5}$

(ii) The quality of dispatched mouth wash is good, but 0.1 of them are defective.

The total percentage of mouthwashes that are good is $(1-0.1) \times 100 = 90 \; \%$