Question

An auditor estimates that $100$ calculators of the 450 calculators manufactured on a particular day by a company are defective. $50$ calculators are tested, out of which $8$ turn out to be defective. Is the auditor's claim accurate?

• A. $Yes$
• B. $No$
• C. $CannotSay$

Answer 1

The correct option is B $No$

Auditor's estimate of faulty calculators $=\frac{100}{450}$

Based on the sampling, faulty calcualator frequency $=\frac{8}{50}$

We now need to compare these two fractions to determine the accuracy of the auditor's claim.

Making the denominators equal for comparison sake,
$\frac{8}{50}=\frac{x}{450}$
$x=\frac{3600}{50}$
$x=72$

Hence we can see that $\frac{72}{450}$ is in fact less than the auditor's claim of $\frac{100}{450}$.

Hence the auditor's claim is inaccurate and the answer is no.