Question

# Roper ASW conducted a survey to learn about American adults’ attitudes toward money and happiness ($Money,$ October $2003$). Fifty-six percent of the respondents said they balance their checkbook at least once a month.What is the probability that the sample proportion will be within $\pm .04$ of the population proportion?

Solution

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Given:

• $n$ = Sample size = 400
• $p$ = Population proportion = 56% = 0.56

In this exercise, we determine the probability $P(|\overline{p}-p|<0.04)$ or equivalently $P(-0.03<\overline{p}-p<0.04)$.

What is the probability distribution of $\overline{p}$?