As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever
A) np ≥5, n ≥30.
B) np ≥5 and n(1-p) ≥5.
C) n 30 and (1 - p) = 0.5.
D) none of these alternatives is correct.

Question

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever
A) np ≥5, n ≥30. 
B) np ≥5 and n(1-p) ≥5. 
C) n 30 and (1 - p) = 0.5. 
D) none of these alternatives is correct.

Quizplus · Accepted Answer

The condition np ≥5 and n(1-p) ≥5 is the most common and widely accepted rule of thumb for approximating the sampling distribution of sample proportions with a normal probability distribution. Alternatively, the condition np ≥5, n ≥30 can also be used, but the second condition is considered a slightly better approximation. Choice C is incorrect because it assumes a specific value for (1-p), which is not always the case in real-world scenarios. Choice D is incorrect because one of the other alternatives is correct.

As a Rule of Thumb, the Sampling Distribution of the Sample