A sample size of 500 is sufficiently large to conclude that the sampling distribution of $\hat { p }$
is a normal distribution,when the estimate of the population proportion is .995.

Question

A sample size of 500 is sufficiently large to conclude that the sampling distribution of $\hat { p }$ 
is a normal distribution,when the estimate of the population proportion is .995.

Quizplus · Accepted Answer

The sample size must satisfy both $np \geq 10$ and $n(1-p) \geq 10$. Here, $n(1-p) = 500 \times 0.005 = 2.5$, which is less than 10, so the condition is not met.

A Sample Size of 500 Is Sufficiently Large to Conclude p^\hat { p }p^​

A Sample Size of 500 Is Sufficiently Large to Conclude $\hat { p }$