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Back to 7.2 Using the Central Limit Theorem

7.2 Exercise 34

Avg difficulty 2.5

A large population has skewed data with a mean of 70 and a standard deviation of 6. Samples of size 100 are taken, and the distribution of the means of these samples is analyzed.

  1. Will the distribution of the means be closer to a normal distribution than the distribution of the population?
  2. Will the mean of the means of the samples remain close to 70?
  3. Will the distribution of the means have a smaller standard deviation?
  4. What is that standard deviation?

OpenStax Introductory Business Statistics 2e, 7.2 Using the Central Limit Theorem, exercise 34

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Adapted from Introductory Business Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Business Statistics 2e. Imported at revision 50ec917.