IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A random sample of n = 36 observations is taken from a population with mean 50 and standard deviation 12. What is the standard deviation of the sample mean?
The standard deviation of the sample mean is 2. It equals the population standard deviation divided by the square root of the sample size, so 12 divided by 6 gives 2.
- A0.33
- B2Correct
- C12
- D6
- 4
Explanation
The standard error of the sample mean is sigma/sqrt(n) = 12/6 = 2. Option 6 uses sqrt(36) alone, and 12 ignores the sample size. Option 4 comes from dividing the variance 144 by 36 and failing to take the square root, and 0.33 comes from 12/36.
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