Statistics 5.6

# Statistics 5.6 - 5-6 Normal as Approximation to Binomial...

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5-6 Normal as Approximation to Binomial Objectives : Students will be able to: Use the normal probability distribution to approximate binomial probabilities. Requirements for a Binomial Distribution Recall that: The procedure must have a fixed number of trials; The trials must be independent; Each trial must have all outcomes classified into two categories; and The probabilities must remain constant for each trial. Theorem: Normal Distribution as an Approximation to the Binomial Distribution If and , then the binomial random variable has a probability distribution that can be approximated by a normal distribution with the mean and standard deviation given as 5 np 5 nq np μ = and npq σ = . Procedure for using a Normal Distribution to Approximate a Binomial Distribution 1. Establish that the normal distribution is a suitable approximation to the binomial distribution by verifying that and . 5 np 5 nq 2. Find the values of the parameters np = and npq = . 3.

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## This note was uploaded on 04/08/2008 for the course MAT 143 taught by Professor Stone during the Spring '07 term at North Shore Community College.

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Statistics 5.6 - 5-6 Normal as Approximation to Binomial...

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