A public relations firm found that only 9 % of voters in a certain state are satisfied with their U.S. senators. How large a sample of voters should be drawn so that the sample proportion $\hat { p }$ of voters who are satisfied with their senators is approximately normally distributed?
A) 11
B) 10
C) 125
D) 112

Question

A public relations firm found that only  9 %  of voters in a certain state are satisfied with their U.S. senators. How large a sample of voters should be drawn so that the sample proportion  $\hat { p }$  of voters who are satisfied with their senators is approximately normally distributed?
A) 11
B) 10
C) 125
D) 112

Quizplus · Accepted Answer

For the sample proportion $\hat{p}$ to be approximately normally distributed, the sample size $n$ must satisfy both $np \geq 10$ and $n(1-p) \geq 10$, where $p = 0.09$ is the proportion of voters satisfied with their senators. Solving for $n$, we find that $n \geq 111.11$. Since $n$ must be an integer, the smallest such $n$ is 112.

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