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IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals

For a normal population with known sigma = 10, an actuary wants a 95% confidence interval for the mean with total width at most 4 (z = 1.96). What is the smallest sample size needed?

The smallest sample size is 97. The width is 2 times 1.96 times 10 divided by root n, which must not exceed 4, so root n is at least 9.8, n is at least 96.04, and rounding up gives 97.

  1. A385Correct
  2. B97
  3. C193
  4. D384
  5. 769

Explanation

Width = 2 x 1.96 x 10/sqrt(n) <= 4, so sqrt(n) >= 39.2/4 = 9.8... recompute: 2x1.96x10 = 39.2; 39.2/4 = 9.8; n >= 96.04, so 97. Hence the correct key is 97, not 385.

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