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Statistics for finance · level 1

68 / 95 / 99.7

Three numbers cover most normal questions asked in an interview. Learn the ladder, then split what is left in half to get a single tail.

Worked example: Normal distribution. What % lie above +1σ?

±1σ68%
±2σ95%
±3σ99.7%
answer16%

Step by step

  1. 1

    The ladder

    ±1σ ≈ 68% · ±2σ ≈ 95% · ±3σ ≈ 99.7%

  2. 2

    One tail is half of what is left

    above +1σ = (100 − 68) / 2 = 16%

  3. 3

    This one

    16%

Normal distribution. What % lie above +1σ? = 16

The theory behind it

Intuition

68/95/99.7 gives you tail probabilities without a table: beyond two sigma is roughly one in twenty, beyond three roughly one in three hundred.

Common pitfalls

  • ×Assuming normality for fat-tailed financial returns.
  • ×Halving the wrong tail when the question is one-sided.

In the interview

Risk framing: how unusual is this month.