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A two-sigma tail probability

EasyRandom VariablesStatistics~3m

XX is Gaussian with mean μ=50\mu = 50 and variance σ2=4\sigma^2 = 4. What is P[X>54]\mathbb{P}[X > 54]? (Give a decimal.)

Show hints (2)+
  1. Standardize: z=(54−50)/σz=(54-50)/\sigma with σ=4=2\sigma=\sqrt4=2.
  2. That is z=2z=2; the one-sided tail P[Z>2]≈0.0228\mathbb{P}[Z>2]\approx 0.0228.

Answer

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0.0228 (± 0.002)

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Asked at: Citadel, DRW

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