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 rule of thumb for approximating the sampling distribution of sample proportions with a normal distribution is np≥5 and n(1-p)≥5. This ensures that there are a sufficient number of successes and failures in the sample, which allows for an accurate approximation of a normal distribution. Additionally, choice A includes n≥30 as a requirement, which is not always necessary for an accurate approximation. Choice C requires (1-p) to be exactly 0.5, which is not always the case in real-world situations. Choice D suggests that none of the alternatives are correct, which is not true as choice B satisfies the necessary conditions for the approximation.

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