CLT for Sums Example

Probability · Axiom Academy

EXAMPLE Central Limit Theorem for Sums Sum of uniform random variables approaches normal distribution Excellent work! You've completed this example. Here's what we learned: CLT applies to sums: The sum of independent random variables approaches a normal distribution, regardless of the original distribution (uniform in this case). Standardization is key: We standardized S₃₀ using Z = (S₃₀ - E[S₃₀])/√Var(S₃₀) to apply normal approximation. Normal approximation: With n=30, the CLT gives an excellent approximation even though the original distribution was uniform, not normal. Practical power: The CLT allows us to approximate difficult probability calculations using standard normal tables. The Central Limit Theorem is one of the most important results in probability, explaining why normal distributions appear so frequently in nature!

This is the written version of the interactive lesson above. See the full Probability course.