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Fifty customers' waiting times were compared with a fitted normal curve, and the two shares below 6.1 minutes came out close. If only 10 customers had been surveyed, what would happen to those two figures?
AThey would move much closer
BThey would match exactly
CThey would move farther apart
DThey would both reach one
Answer & Solution
Correct answer: C. They would move farther apart
1. A normal curve is a smooth model laid over real, lumpy data.
2. With 50 customers the data trace that smooth shape reasonably well.
3. The two shares came out close for exactly that reason.
4. A sample of only 10 gives far fewer values to fill in the shape.
5. Ten values leave gaps and bumps that a smooth curve cannot follow.
6. So the model fits worse and the two figures drift farther apart.
7. They cannot match exactly, since real data never trace a smooth curve perfectly.
8. Neither figure heads towards one, because that would mean every customer waited under 6.1 minutes.
_Source: OpenStax High School Statistics (CC BY 4.0), section 6.2 Using the Normal Distribution_
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