Getting ready for work

How to use normal distributions to plan a reliable commute

This is an easy statistics question that tests your intuition for the normal distribution and how its parameters affect tail probabilities. It's the kind of practical reasoning quant firms expect candidates to apply when thinking about risk, lateness, or operational constraints.

The question asks you to reason about which of two levers—the mean or the standard deviation—has the stronger effect on the probability of being late. To solve it, you'll need to recall how the normal distribution is standardised, what quantiles tell you about tail behaviour, and how much margin you need to build in order to hit a specific confidence target. The goal is to decide which parameter change allows you to leave as late as possible and still arrive on time with high probability.

• Standardising normal random variables and z-scores
• Quantiles and confidence intervals
• How mean and variance trade off in risk management