# Activities

• • • ##### Subject Area

• Math: Statistics: Sampling Distributions

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™ CX
TI-Nspire™ CX CAS

5.0

• ##### Report an Issue

Central Limit Theorem

Updated on 06/11/2019

#### Activity Overview

This lesson involves examining distributions of sample means of random samples of size n from four different populations.

#### Objectives

• Students will recognize that when n is sufficiently large, the sampling distribution of sample means, x̄, is approximately normal, regardless of the shape of the population distribution (Central Limit Theorem).
• Students will recognize that when the population distribution is normal, the sampling distribution of sample means, x̄, is normal for any sample size n.
• Students will recognize the consequences of the Central Limit Theorem when applied to quantitative data: a normal model with μ = μ (the true population mean) and that decreases as sample size, n, increases.
• Students will recognize the consequences of the Central Limit Theorem when applied to proportions: a normal model with μ = P (the true population proportion) and σ that decreases as sample size, n, increases.

#### Vocabulary

• Central Limit Theorem (CLT)
• normal distribution
• population
• proportion
• quantitative data
• sample
• sample mean
• sample proportion
• sampling distribution
• skewed right distribution