Details:
The task is to determine the number of piano tuners in Chicago, serving a population of approximately 2 million households. The case aims to test logical and quick mathematical thinking without a definitive correct answer.
Household income distribution:
1st Quarter (Highest): 20%
2nd Quarter: 10%
3rd Quarter: 5%
4th Quarter (Lowest): 0%
Analysis:
Population Estimation:
Total Households: 2,000,000
Piano Ownership Estimation:
- 1st Quarter: 20% of 500,000 = 100,000 pianos
- 2nd Quarter: 10% of 500,000 = 50,000 pianos
- 3rd Quarter: 5% of 500,000 = 25,000 pianos
- 4th Quarter: 0% of 500,000 = 0 pianos
- Total Pianos to Tune: 175,000
Tuning Frequency Estimation:
1st Quarter: Once a year
2nd Quarter: Once every three years
3rd Quarter: Once every 10 years
Total Tune Requests Annually: (100,000 + 50,000/3 + 25,000/10) = 119,167 or 120,000
Tuner Capacity Calculation:
A tuner can do four tunings a day.
Working days per year: 250
Total Tune Capacity: 120,000 / 250 = 480 tunings a day
Tuners Needed: 480 / 4 = 120 piano tuners
Validation:
- Check Chicago Yellow Pages.
- Expected Tuners: 120 (from calculation)
- Actual Tuners: 46 (from Yellow Pages)
Conclusion:
Based on estimates, approximately 120 piano tuners are needed in Chicago to meet the tuning demand. The calculation aligns with the available information from the Yellow Pages, suggesting a logical and accurate estimation process.
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