Data Science

Standard Normal Distribution and Z-Scores

Arun Murali

Tags: data-science; distributions; statistics; standardization

🟪 1-Minute Summary

The standard normal distribution is a special case of the normal distribution with mean = 0 and standard deviation = 1. Z-scores transform any normal distribution to this standard form, allowing you to compare values from different distributions and look up probabilities in standard tables. Formula: z = (x - μ) / σ.

🟦 Core Notes (Must-Know)

What is the Standard Normal Distribution?

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Z-Score Formula and Interpretation

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When to Use Z-Scores

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Z-Table (Standard Normal Table)

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🟨 Interview Triggers (What Interviewers Actually Test)

Common Interview Questions

  1. “A student scored 85 on a test with mean=75 and SD=10. What’s their z-score?”

    • [Answer: z = (85-75)/10 = 1.0]

  2. “Why do we standardize data?”

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🟥 Common Mistakes (Traps to Avoid)

Mistake 1: Forgetting the sign of the z-score

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Mistake 2: Using z-scores for non-normal data

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🟩 Mini Example (Quick Application)

Scenario

[Comparing test scores from different classes]

Solution

import numpy as np
from scipy import stats

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🔗 Related Topics

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