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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

Annual losses on a loan portfolio per account are independent with mean 200 and standard deviation 600 (USD). For a pool of 900 accounts, using the CLT, what is the approximate probability that the average loss per account exceeds 230? (Use the standard normal: P(Z>1)=0.1587, P(Z>1.5)=0.0668, P(Z>2)=0.0228, P(Z>0.5)=0.3085.)

The probability is about 0.0668. The standard error is 600 divided by 30, which is 20, so the z-score for 230 is (230-200)/20 = 1.5. The upper-tail probability of a standard normal beyond 1.5 is 0.0668.

  1. A0.3085
  2. B0.1587Correct
  3. C0.0668
  4. D0.0228

Explanation

Standard error = 600/sqrt(900) = 600/30 = 20. Z = (230-200)/20 = 1.5, so the probability is P(Z>1.5)=0.0668. Wait: this gives 0.0668, so the correct option is 0.0668. Using the 600 standard deviation instead of the standard error gives Z=0.05-level results and the 1.0 value 0.1587 arises from an erroneous standard error of 30.

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