What percent of our products arrive at the customer with defects?
Understand the Problem
The question is asking to calculate the percentage of products that arrive at the customer with defects, based on the given defect rates for on-time and late shipments.
Answer
The percentage of products that arrive at the customer with defects is $11\%$.
Answer for screen readers
The percentage of products that arrive at the customer with defects is 11%.
Steps to Solve
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Determine the number of on-time and late products Since 90% of the products are shipped on time, we can calculate:
- On-time products: $$ 0.9 \times 100 = 90 \text{ products} $$
- Late products: $$ 100 - 90 = 10 \text{ products} $$
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Calculate defective on-time products The customer states that 10% of the on-time products are defective. Thus: $$ 0.1 \times 90 = 9 \text{ defective on-time products} $$
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Calculate defective late products The customer indicates that 20% of all products shipped late are defective. Therefore: $$ 0.2 \times 10 = 2 \text{ defective late products} $$
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Total defective products Now, we sum the defective products from both shipments: $$ 9 + 2 = 11 \text{ defective products} $$
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Calculate the percentage of defective products Finally, we find the percentage of all products that are defective: $$ \text{Percentage} = \left( \frac{11}{100} \right) \times 100 = 11% $$
The percentage of products that arrive at the customer with defects is 11%.
More Information
This calculation indicates that a notable proportion of the total products shipped were found to be defective. Understanding these rates helps in quality control and customer satisfaction.
Tips
- Miscalculating the number of on-time or late products. Always be sure to apply the percentages to the correct total.
- Failing to properly apply the percentages to the subgroups (on-time vs late) before summing them for the final calculation.
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