IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A random sample of n = 25 observations is taken from a population with mean 40 and variance 100. What is the standard deviation of the sample mean?
The standard deviation of the sample mean is 2. The variance of the sample mean equals the population variance divided by n, which is 100/25 = 4, and its square root is 2.
- A0.4
- B2Correct
- C4
- D10
- 20
Explanation
Var(X̄) = σ²/n = 100/25 = 4, so the standard deviation is 2. Option 4 is the variance of X̄, not its standard deviation. Option 10 is the population standard deviation, which ignores the division by n.
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