🟪 1-Minute Summary
The normal distribution (bell curve) is a symmetric, continuous probability distribution defined by its mean (μ) and standard deviation (σ). It’s the foundation of many statistical methods because many natural phenomena approximate it, and the Central Limit Theorem says sample means tend toward normality. The 68-95-99.7 rule describes how data spreads.
🟦 Core Notes (Must-Know)
What is the Normal Distribution?
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Key Properties
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The 68-95-99.7 Rule (Empirical Rule)
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Parameters: μ (mean) and σ (standard deviation)
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Why It Matters
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🟨 Interview Triggers (What Interviewers Actually Test)
Common Interview Questions
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“What percentage of data falls within 2 standard deviations of the mean in a normal distribution?”
- [Answer: ~95%]
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“Why is the normal distribution so important in statistics?”
- [Answer framework: Central Limit Theorem, hypothesis testing assumptions]
🟥 Common Mistakes (Traps to Avoid)
Mistake 1: Assuming all data is normally distributed
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Mistake 2: Confusing standard normal with general normal
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🟩 Mini Example (Quick Application)
Scenario
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Solution
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
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