when i can use Normal approximation of the binomial distribution ? how can i know form examples ?

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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when i can use Normal approximation of the binomial distribution ?

how can i know form examples ?

Expert Solution
Step 1

Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials being independent and the probability of success, say p, remaining constant, then the distribution of the number of success follows binomial.

Let us assume X be a random variable denoting the number of success.

Then X~bin(n, p), n and p being the parameters of the binomial distribution.

The probability mass function of X is given by,

Statistics homework question answer, step 1, image 1

Normal Distribution: A continuous random variable X is said to follow Normal distribution with parameters μ and σ2 if its probability density function is given by,

Statistics homework question answer, step 1, image 2

It is denoted by,

Statistics homework question answer, step 1, image 3

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