Question

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

What is the probability of getting $150$customers in one day?

Short answer

The probability of getting$150$customers in one day at the clothing store is $0.001$

Step-by-step solution

Concept used

The conditions for astatistical distribution are:
i.the amount of trials, $n$is incredibly large, and
ii. The probability of success, $p$is extremely small.
such that $np$could be a finite quantity.
Thus, the probability of $x$successes is given by:
$P(X=x)=\frac{e^{-\lambda }{\lambda }^x}{x!};x=0,1,2,\dots \dots \&\lambda >0$
where $\lambda$is that the mean of the distribution.

Given

On an average $120$customers arrive at the store per day.

Calculation 

The random variable $X$follows the Poisson distribution with parameter $\lambda (X~P(\lambda \left)\right)$as it satisfies all the condition for a Poisson distribution.

Thus, the required probability is given by,

$P(X=150)=0.001$. (Since the value of $\lambda$is very large, this probability can only be calculated using a computer or a calculator).