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# calculating the probability for population proportion

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Roper ASW conducted a survey to learn about American adults' attitudes toward money and happiness. 56% of the respondents said they balance their checkbook at least once a month.

a. Suppose a sample of 400 American adults were taken. Show the sampling distribution of the proportion of adults who balance their checkbook at least once a month .
b. What is the probability that the sample proportion will be within Â± .02 of the population proportion?
c. What is the probability that the sample proportion will be within Â± .04 of the population proportion?

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#### Solution Preview

a. By the central limit theorem, the sampling distribution of proportion is normal with mean 0.56 and variance=56%*(1-56%)/400=0.000616

b. The lower limit of the sample proportion which is less than or equal to 0.02 from the population proportion = 0.56-0.02 = 0.54
The upper limit ...

#### Solution Summary

The solution gives detailed steps on calculating the probability for population proportion under different conditions.

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