For $n$ sufficiently large, and p sufficiently close to $0.5$, the distribution of $\frac { \hat { p } - p } { \sigma _ { \hat { p } } }$ is approximately a standard normal distribution.

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Quizplus · Accepted Answer

This is a statement of the central limit theorem, which states that the distribution of sample means (or proportions) approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. Therefore, for sufficiently large sample sizes and values of p close to 0.5 (which ensures that the sample proportion is not too skewed), the distribution of the standardized sample proportion will be approximately standard normal.

For nnn Sufficiently Large, and P Sufficiently Close To 0.50.50.5 , the Distribution Of

For $n$ Sufficiently Large, and P Sufficiently Close To $0.5$ , the Distribution Of