Year Type-B Production (in '000) Type-B Defect-free (%) Type-C Production (in…

Concept

The defect-free count for a given year and type equals that year's production multiplied by the defect-free percentage for that type and year. The average defect-free count for a type over several years is the sum of each year's defect-free count divided by the number of years.

Application

1. Compute Type-B's defect-free count for each year: 2019 = 40 × 96% = 38.4 ('000); 2020 = 55 × 92% = 50.6 ('000); 2021 = 50 × 95% = 47.5 ('000); 2022 = 45 × 94% = 42.3 ('000).

2. Sum Type-B's four yearly values: 38.4 + 50.6 + 47.5 + 42.3 = 178.8 ('000), then divide by 4 to get the average: 178.8 / 4 = 44.7 ('000) = 44,700 units.

3. Compute Type-C's defect-free count for each year: 2019 = 60 × 90% = 54.0 ('000); 2020 = 52 × 93% = 48.36 ('000); 2021 = 48 × 92% = 44.16 ('000); 2022 = 50 × 88% = 44.0 ('000).

4. Sum Type-C's four yearly values: 54.0 + 48.36 + 44.16 + 44.0 = 190.52 ('000), then divide by 4 to get the average: 190.52 / 4 = 47.63 ('000) = 47,630 units.

5. Subtract Type-B's average from Type-C's average to get the required difference: 47,630 − 44,700 = 2,930.

Cross-check

As an independent check, since averaging is linear, the difference between the two four-year averages equals the average of the four yearly differences: (54.0 − 38.4) + (48.36 − 50.6) + (44.16 − 47.5) + (44.0 − 42.3) = 15.6 + (−2.24) + (−3.34) + 1.7 = 11.72; dividing by 4 gives 11.72 / 4 = 2.93 ('000) = 2,930, which exactly matches the result above.

Therefore, the required difference is 2,930.