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

A random variable X is normally distributed with a mean of 8 and a standard deviation of 4. Using Φ(1) = 0.8413, Φ(2) = 0.9772 and Φ(3) = 0.9987, what is P(X > 16)?

The probability is 2.28%. The value 16 lies two standard deviations above the mean of 8, so z = 2, and the upper-tail probability is 1 − 0.9772 = 0.0228. Doubling it for both tails or using the lower tail would be incorrect.

  1. A2.28%Correct
  2. B4.55%
  3. C15.87%
  4. D97.72%

Explanation

The standardized value is z = (16 − 8)/4 = 2. The upper-tail probability is 1 − Φ(2) = 1 − 0.9772 = 0.0228. The 4.55% option is the two-tailed probability, and 97.72% is the lower tail.

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