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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 ± .02 of the population proportion?
    c. What is the probability that the sample proportion will be within ± .04 of the population proportion?

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    https://brainmass.com/statistics/descriptive-statistics/calculating-the-probability-for-population-proportion-557551

    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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