Quant interview prep guides

Normal Distribution Mental Math

Normal distribution mental math for estimating ranges, z-score landmarks, tail probabilities, and approximation caveats in interviews.

Candidates working on statistics, risk, and research interview prompts.

Use landmark ranges

For a normal distribution, about 68 percent lies within one standard deviation and about 95 percent lies within two. These are landmarks, not proof that a variable is normal.

Convert to z-scores

Subtract the mean and divide by standard deviation to put a value on a standard scale. This makes different distributions easier to compare.

Concrete example

If mean is 100 and standard deviation is 15, a value of 130 is two standard deviations above the mean. Under a normal model, that is in the upper tail.

Check assumptions

Normal approximations can be useful, but some interview variables are skewed, bounded, or heavy-tailed. Mention the approximation before using it.

Common mistakes

Candidates often apply normal landmarks to every distribution. First ask whether the normal model is stated, justified, or merely a rough approximation.

Practice the pattern

Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.