Lesson 28: Approximations for Discrete Distributions

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Introduction

In the previous lesson, we explored the Central Limit Theorem, which states that if X1, X2, ... , Xn is a random sample of "sufficient" size n from a population whose mean is μ and standard deviation is σ, then:

\(Z=\dfrac{\bar{X}-\mu}{\sigma/\sqrt{n}}=\dfrac{\sum\limits_{i=1}^n X_i-n\mu}{\sqrt{n}\sigma} \stackrel {d}{\longrightarrow} N(0,1)\)

In that lesson, all of the examples concerned continuous random variables. In this lesson, our focus will be on applying the Central Limit Theorem to discrete random variables. In particular, we will investigate how to use the normal distribution to approximate binomial probabilities and Poisson probabilities.

Objectives

  • To learn how to use the normal distribution to approximate binomial probabilities.
  • To learn how to use the normal distribution to approximate Poisson probabilities.
  • To be able to apply the methods learned in this lesson to new problems.