$$\mathrm { N } = 24,000 , \mathrm { n } = 400 , \mathrm { p } = 0.7$$
A) Approximately normal; $\mu _ { \mathrm { p } } = 0.7 , \sigma \mathrm { p } = 0.023$
B) Exactly normal; $\mu _ { \mathrm { p } } = 0.7 , \sigma _ { \mathrm { p } } = 0.023$
C) Approximately normal; $\mu _ { \mathrm { p } } = 0.7 , \sigma _ { \mathrm { p } } = 0.0935$
D) Binomial; $\mu _ { \mathrm { p } } = 280 , \sigma _ { \mathrm { p } } = 9.17$ Provide an appropriate response.

Question

Quizplus · Accepted Answer

The distribution is approximately normal due to the large sample size (n = 400) and the use of the sample proportion (p = 0.7). The mean ($\mu_p$) of the sample proportion is indeed 0.7, and the standard deviation ($\sigma_p$) can be calculated using the formula for the standard deviation of a sample proportion: $\sigma_p = \sqrt{\frac{p(1-p)}{n}}$, which gives approximately 0.023 when p = 0.7 and n = 400.

N=24,000,n=400,p=0.7\mathrm { N } = 24,000 , \mathrm { n } = 400 , \mathrm { p } = 0.7N=24,000,n=400,p=0.7

$\mathrm { N } = 24,000 , \mathrm { n } = 400 , \mathrm { p } = 0.7$