A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of is
A)not normal since n $\lt$ 30
B)approximately normal because is always normally distributed
C)approximately normal if np $\ge$ 5 and n(1-p) $\ge$ 5
D)approximately normal if np $\gt$ 30 and n(1-p) $\gt$ 30

Question

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of  is
A)not normal since n $\lt$ 30 
B)approximately normal because is always normally distributed 
C)approximately normal if np $\ge$ 5 and n(1-p) $\ge$ 5 
D)approximately normal if np $\gt$ 30 and n(1-p) $\gt$ 30

Quizplus · Accepted Answer

The sampling distribution of the mean can be approximated to a normal distribution if both np and n(1-p) are greater than or equal to 5. This is known as the Central Limit Theorem. Therefore, choice C is the best choice as it includes this condition. The other choices either do not include this condition or have more stringent conditions that might not be met by the sample.

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