Question

An auditor estimates that $100$ of $450$ calculators manufactured on a particular day are defective. $50$ calculators are tested, out of which $8$ are defective. Is the auditor's claim accurate? If not, how many calculators have to be defective to make his claim accurate?

• A. Cannot be determined
• B. Yes
• C. No, $72$
• D. No, $28$

Answer 1

The correct option is C No, $72$

Auditor's estimate of faulty calculators $=\frac{100}{450}$
Frequency of faulty calculators based on sampling $=\frac{8}{50}$

We now need to compare these two fractions to determine the accuracy of the auditor's claim.
$\frac{8}{50}=\frac{x}{450}$
$x=\frac{3600}{50}$
$x=72$
We can see thet $\frac{72}{450}$ is less than the auditor's claim of $\frac{100}{450}$.
Hence, the auditor's claim in inaccurate and the answer is no.