The Central Limit Theorem says that if a number of probability distributions are summed:
A)The standard deviation of the sum equals the sum of the standard deviations.
B)The variance of the sum equals the sum of the variances.
C)The standard deviation of the sum is greater than the sum of the standard deviations.
D)The variance of the sum is less than the sum of the variances.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that as the number of independent, identically distributed random variables summed together increases, the distribution of their sum approaches a normal distribution. The theorem also states that the variance of the sum of these variables is equal to the sum of their variances. Therefore, choice B is correct. The standard deviation of the sum is the square root of the variance, so choice A and C are incorrect. Choice D is also incorrect because the variance of the sum is equal to the sum of the variances, not less than the sum of the variances.

The Central Limit Theorem Says That If a Number of Probability