What is the standard deviation if a proportion of 0.89 of nonconforming items is found from twelve samples of size 136,twelve samples of size 124,and thirty samples of size 131?
A)0.027
B)0.001
C)0.566
D)0.305

Question

Quizplus · Accepted Answer

The standard deviation of a proportion for samples of different sizes can be calculated using the formula $\sqrt{p(1-p)(\frac{1}{n_1}+\frac{1}{n_2}+\cdots+\frac{1}{n_k})}$, where $p$ is the proportion of nonconforming items, and $n_1, n_2, \ldots, n_k$ are the sizes of the samples. Given $p = 0.89$, twelve samples of size 136, twelve samples of size 124, and thirty samples of size 131, the calculation is $\sqrt{0.89 \times (1-0.89) \times (12/\!136 + 12/\!124 + 30/\!131)}$, which approximates to 0.027.

What Is the Standard Deviation If a Proportion of 0