Suppose a random sample of $\mathrm { n }$ measurements is selected from a binomial population with probability of success $p = .35$. Given $n = 200$, describe the shape, and find the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$.
A) skewed right; $0.35,0.034$
B) approximately normal; $0.35,0.034$
C) approximately normal; $0.35,0.0011$
D) skewed right; $70,6.75$

Question

Quizplus · Accepted Answer

The sampling distribution of the sample proportion $\hat{p}$ will be approximately normal due to the large sample size (n = 200) and the use of the Central Limit Theorem. The mean of the sampling distribution is equal to the population proportion $p = 0.35$. The standard deviation of the sampling distribution is calculated using the formula $\sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.35(0.65)}{200}} \approx 0.034$.

Suppose a Random Sample Of n\mathrm { n }n Measurements Is Selected from a Binomial Population with Probability of Is

Suppose a Random Sample Of $\mathrm { n }$ Measurements Is Selected from a Binomial Population with Probability of Is