IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem
Independent observations each have variance 64. A sample mean must have standard deviation at most 1.0 to meet a precision target. What is the smallest sample size n that meets it?
The smallest sample size is 64. The standard deviation of the sample mean is 8 divided by the square root of n, and setting this at most 1 requires the square root of n to be at least 8, so n is at least 64.
- A8
- B32
- C64Correct
- D128
- 16
Explanation
SD of mean = 8/sqrt(n) <= 1 gives sqrt(n) >= 8, so n >= 64. Choosing 8 confuses n with the standard deviation; 128 doubles unnecessarily.
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