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Normal distribution

As explained in Experimentation for Engineers

A continuous probability distribution characterized by a symmetric bell-shaped curve determined by its mean and standard deviation.

A normal distribution is a symmetric bell-shaped model. In A/B testing, aggregate measurement scores are treated as approximately normal, enabling probability thresholds for engineering decisions. section 2.3.1

The unit normal has mean zero and standard deviation one. For a one-sided 5% threshold, 5% of its area falls below z = -1.64; values farther left indicate statistical significance under the test’s assumptions. section 2.3.1

Choosing between trading venues

Compare aggregate execution costs for ASDAQ and BYSE, compute the difference and its standard error, then form z. If z < -1.64, act as though BYSE is better; otherwise keep ASDAQ. The normal approximation improves as the number of individual measurements grows, but the decision remains a bet rather than a certainty. section 2.3.1

How Experimentation for Engineers covers it

How deep it goes
Defines the unit normal and threshold, then qualifies normality as an improving approximation from the central limit theorem.
Examples
Uses aggregate execution costs, ASDAQ-versus-BYSE comparisons, and the z = -1.64 cutoff.
What you can do after
Evaluate whether an aggregate A/B-test measurement crosses a chosen statistical threshold.
How it connects
Connects z-scores, standard deviation, central limit theorem, statistical significance, and A/B testing.
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