Question

each day, a fedex competitor processes approximately 65,000 shipments. suppose that they use the same service quality index as fedex and identified the following number of errors during a 5-day week (see the \fedex: measuring service performance\ box). these values are hypothetical and do not reflect any real company’s actual performance.

description	weight	number of errors
damaged packages	10	20
international	1	103
invoice adjustments	1	286
late pickup stops	3	204
lost packages	10	1
missed proof of delivery	1	26
right date late	1	747
traces	3	110
wrong day late	5	20

compute the service quality indicator by finding the weighted sum of errors as a percentage of total shipments. do not round intermediate calculations. round your answer to three decimal places.

service quality indicator (sqi): %

Explanation:

Step1: Calculate weighted errors for each category

For each row, multiply Weight by Number of Errors:

• Complaints reopened: $3\times145 = 435$
• Damaged packages: $10\times20 = 200$
• International: $1\times103 = 103$
• Invoice adjustments: $1\times286 = 286$
• Late pickup stops: $3\times204 = 612$
• Lost packages: $10\times1 = 10$
• Missed proof of delivery: $1\times26 = 26$
• Right date late: $1\times747 = 747$
• Traces: $3\times110 = 330$
• Wrong day late: $5\times20 = 100$

Step2: Sum all weighted errors

Add all the weighted errors: $435 + 200 + 103 + 286 + 612 + 10 + 26 + 747 + 330 + 100 = 2849$

Step3: Calculate total shipments for 5 days

Daily shipments: 65,000, so 5 - day total: $65000\times5 = 325000$

Step4: Compute SQI as (weighted sum / total shipments) × 100

$SQI=\frac{2849}{325000}\times100$
Calculate $\frac{2849}{325000}=0.00876615\cdots$
Multiply by 100: $0.00876615\cdots\times100 = 0.876615\cdots$

Step5: Round to three decimal places

Rounded value: $0.877$

Answer:

$0.877$