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
The ladder
±1σ ≈ 68% · ±2σ ≈ 95% · ±3σ ≈ 99.7%
- 2
One tail is half of what is left
above +1σ = (100 − 68) / 2 = 16%
- 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.