Question

question 1 a quality assurance analyst reviews the table and calculations for all three products. he concludes that there is a significant problem with the overall failure rate of 22.92%. a second analyst reviews the same table and calculations. at which step will this analyst find an error? products # of trials # of successes a 500 450 b 400 375 c 300 280 product a: \\(\frac{500 - 450}{500} = \frac{50}{500} = 10\\%\\) product b: \\(\frac{400 - 375}{400} = \frac{25}{400} = 6.25\\%\\) product c: \\(\frac{300 - 280}{300} = \frac{20}{300} \approx 6.67\\%\\) overall failure rate: \\(10\\% + 6.25\\% + 6.67\\% = 22.92\\%\\) \\(\circ\\) a) checking the data for recording errors \\(\circ\\) b) checking the formula and order of operations \\(\circ\\) c) checking the calculations \\(\circ\\) d) the work is correct.

Explanation:

Step1: Calculate total trials

$500 + 400 + 300 = 1200$

Step2: Calculate total failures

$(500-450)+(400-375)+(300-280) = 50 + 25 + 20 = 95$

Step3: Calculate correct overall failure rate

$\text{Overall Failure Rate} = \frac{95}{1200} \times 100\% \approx 7.92\%$

Step4: Identify error source

The original calculation incorrectly summed individual failure rates instead of using total failures over total trials. This is a formula/operation order error.

Answer:

B) checking the formula and order of operations