Lesson 10: Sampling Distributions and the Central Limit Theorem

September 30, 2025

Review:

• Survey Project
• Enter Survey Link

Presentation:

• The Sampling Distribution of a Sample Mean
  • Take multiple Simple Random Samples, sample size = n, and calculate each sample mean
  • “Sampling Distribution” is the distribution of sample means
  • Standard deviation of sample means = s/√n
• Central Limit Theorem (CLT)
  • Simple random samples of size n from any population with mean μ and finite standard distribution σ. When n is large (typically ≥ 30), the sampling distribution of the sample mean is approximately Normal.
• Video: Sampling Distributions

Activity:

• Coin toss
  • Toss a coin 10x
  • Count the number of times the coin turns up “Heads”
• Dice roll
  • Roll a pair of dice (6-sided) 10x
  • Add up the total for all 10 rolls
• Demo CLT with Coin Flip, Dice Roll and Commute Time