# When can the Poisson distribution be used to approximate the binomial distribution?

Table of Contents

- 1 When can the Poisson distribution be used to approximate the binomial distribution?
- 2 Why would you want to use the normal distribution to approximate a binomial distribution?
- 3 What is the difference between Normal and Poisson distribution?
- 4 Why and under what conditions is the normal distribution usually used as an approximation to the binomial and Poisson distribution?
- 5 How do you approximate Poisson to normal?
- 6 When can we use the normal approximation to the binomial?

## When can the Poisson distribution be used to approximate the binomial distribution?

Poisson Approximation to the Binomial When the value of n in a binomial distribution is large and the value of p is very small, the binomial distribution can be approximated by a Poisson distribution. If n > 20 and np < 5 OR nq < 5 then the Poisson is a good approximation.

## Why would you want to use the normal distribution to approximate a binomial distribution?

The normal approximation allows us to bypass any of these problems by working with a familiar friend, a table of values of a standard normal distribution. Many times the determination of a probability that a binomial random variable falls within a range of values is tedious to calculate.

**When can you approximate binomial with Normal?**

When n * p and n * q are greater than 5, you can use the normal approximation to the binomial to solve a problem.

### What is the difference between Normal and Poisson distribution?

Normal distribution describes continuous data which have a symmetric distribution, with a characteristic ‘bell’ shape. Poisson distribution describes the distribution of binary data from an infinite sample. Thus it gives the probability of getting r events in a population.

### Why and under what conditions is the normal distribution usually used as an approximation to the binomial and Poisson distribution?

Binomial Approximation The normal distribution can be used as an approximation to the binomial distribution, under certain circumstances, namely: If X ~ B(n, p) and if n is large and/or p is close to ½, then X is approximately N(np, npq)

**When can we approximate binomial with normal?**

#### How do you approximate Poisson to normal?

Poisson(100) distribution can be thought of as the sum of 100 independent Poisson(1) variables and hence may be considered approximately Normal, by the central limit theorem, so Normal( μ = rate*Size = λ*N, σ =√(λ*N)) approximates Poisson(λ*N = 1*100 = 100).

#### When can we use the normal approximation to the binomial?

**Why is there a difference between normal approximation and exact method?**

Most textbooks use the normal approximation method because it is easy for students to calculate manually. However, the exact methods are usually more reliable than the normal approximation method. With the normal approximation, it is possible to get different conclusions between the p-value and the confidence interval.