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# Suppose we know that the proportion of objects in a population that have a particular characteristic ...

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Suppose we know that the proportion of objects in a population that have a particular characteristic of interest is 0.10. Are there any concerns if we want to calculate probabilities for the sampling distribution of$$\style{font-family:Times New Roman;}{\widehat p}$$ n= 40 using a normal approximation?

Becausenis large, our only concern with using a normal approximation will be the small amount of variability in the sampling distribution of$$\style{font-family:Times New Roman;}{\widehat p}$$.

Because$$\style{font-family:Times New Roman;}{\;n}$$is small here, the sampling distribution of$$\style{font-family:Times New Roman;}{\widehat p}$$should not be assumed to be approximately normal.

Because$$\style{font-family:Times New Roman;}{\widehat p}$$ ≤ 0.5, the sampling distribution of$$\style{font-family:Times New Roman;}{\widehat p}$$should not be assumed to be approximately normal.

If $$\style{font-family:Times New Roman;}{\widehat p}$$ < 5, then a normal approximation is not appropriate.

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## Introductory Statistics: A Problem-Solving Approach

Edition: 3rd
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isaw09isaw09
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