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**CFA Practice Question**

Which of the following is correct?

A. If we know the population variance, then the Central Limit Theorem enables us to calculate the variance of the distribution of the estimator for the mean of a large sample.

B. The range for a discrete distribution A is twice as much for a discrete distribution B. The standard deviation of A is necessarily larger than the standard deviation of B.

C. The mean of a large sample minus the mean of the population (from which the sample has been taken) has a t-distribution.

**Explanation:**One can easily have a situation where discrete distribution A has two extreme values and the rest of the values lumped close together, therefore giving a large range but small standard deviation.

The mean of a population is non-random, whereas the mean of a large sample has a normal distribution (from CLT). Therefore the mean of a large sample minus the mean of the population (from which the sample has been taken) has a normal distribution.

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**User Contributed Comments**
1

User |
Comment |
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birdperson |
wording on this question is really tricky |