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

Quizplus · Accepted Answer

The central limit theorem states that for a sufficiently large sample size (n), the sampling distribution of sample proportions can be approximated by a normal distribution with mean = p and standard deviation = sqrt(p(1-p)/n). 
Choice A is incorrect because it does not provide any information about the value of p, which is needed to calculate the mean and standard deviation of the sampling distribution. 
Choice C is incorrect because it assumes that (1-p) = 0.5, which may not be true in all cases. 
Choice D is incorrect because there is a condition where the central limit theorem applies, as stated in choice B.

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