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A normal curve fitted to 60 stadium capacities and the actual count of stadiums give slightly different shares below 67,000 seats. Why do the two differ?
AThe data were counted wrongly
BThe curve is only an approximation
CThe mean was set far too high
DThe sample was far too large
Answer & Solution
Correct answer: B. The curve is only an approximation
1. Counting the real stadiums gives the exact share in that sample.
2. Reading the fitted normal curve gives a smooth model of the same data.
3. Real data never trace a smooth curve perfectly, so the two figures land close but not equal.
4. The gap is a sign that the model is an approximation, not that anyone miscounted.
_Source: OpenStax High School Statistics (CC BY 4.0), section 6.2 Using the Normal Distribution_
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