Question

Use the following information to answer the next six exercises: On average, a clothing store gets $120$customers per day.

Which type of distribution can the Poisson model be used to approximate? When would you do this?

Short answer

The Poisson model can be approached by a Binomial distribution when the number of trials,$n$ is veritably large and probability of success,$p$ is veritably small.

Step-by-step solution

Introduction 

We formerly know that both Binomial and Poisson distributions are used when the arbitrary variable of interest is separate and measures the' number of successes'. Still, when the arbitrary trial is similar that

i. The number of trials, $n$is veritably large ( generallylocalid="1649712627472" $>20$) i.e.localid="1649712634391" $n\to \infty$

Explanation

ii. The probability of success, is veritably small ( generally$<0.05$) i.e.,$p\to 0$
similar that np becomes a finite volume, also Poisson model is used to compare the Binomial distribution.
Let$np=\lambda$which is the mean of the distribution and is finite.