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CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing

An analyst draws many random samples of size 50 from a population that is clearly right-skewed with a finite mean and variance. According to the central limit theorem, the distribution of the sample means is most likely:

The sample means will be approximately normally distributed and centered on the population mean. The central limit theorem says this holds for large random samples from any population with finite variance, even a skewed one, and the variance of the sample mean shrinks as the sample size grows.

  1. Aapproximately normal, with a mean equal to the population meanCorrect
  2. Bskewed in the same way as the population, with a mean below the population mean
  3. Cuniform, with a variance equal to the population variance

Explanation

For a large random sample from a population with finite variance, the sampling distribution of the mean is approximately normal and centered on the population mean, whatever the population shape. The skewed option ignores the theorem, and the sample-mean variance is the population variance divided by n, not equal to it.

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