Which of the following best describes the form of the sampling distribution of the sample proportion?
A)When standardized,it is exactly the standard normal distribution.
B)When standardized,it is the t distribution.
C)It is approximately normal as long as n $\ge$30.
D)It is approximately normal as long as np $\ge$5 and n(1-p)$\ge$5.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample proportion is approximately normal when both np and n(1-p) are greater than or equal to 5, which is the condition stated in option D. It is not exactly the standard normal distribution (option A) and not the t-distribution (option B). Option C is partially correct since it states the condition for normality only for a large sample size of n>30, but it does not include the condition for the success-failure rule. Therefore, option D is the best choice.

Which of the Following Best Describes the Form of the Sampling