A sample of 25 observations is taken from an infinite population.The sampling distribution of is A) not normal since n 30 and n(1- P) 30.

Question

A sample of 25 observations is taken from an infinite population.The sampling distribution of  is
A) not normal since n < 30. 
B) approximately normal because is always normally distributed. 
C) approximately normal if np 5 and n(1-
P) 5. 
D) approximately normal if np > 30 and n(1-
P) > 30.

Quizplus · Accepted Answer

The given sampling distribution is that of a proportion, which is approximately normal if np and n(1-P) are both greater than or equal to 5. Therefore, option C is the best choice. Options A and D can be eliminated as they make incorrect claims about the normality of the distribution. Option B is incorrect as the fact that 11eb12ba_eac2_4818_94c2_f9687b49e36a_TB6982_11 is normally distributed does not guarantee that its sampling distribution (in this case, the proportion) will also be normal.

A Sample of 25 Observations Is Taken from an Infinite