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Chapter 4: Q. 58 (page 287)

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

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

Short Answer

Expert verified

The probability of getting150customers in one day at the clothing store is 0.001

Step by step solution

01

Concept used

The conditions for astatistical distribution are:
i.the amount of trials, nis incredibly large, and
ii. The probability of success, pis extremely small.
such that npcould be a finite quantity.
Thus, the probability of xsuccesses is given by:
P(X=x)=e-λλxx!;x=0,1,2,……&λ>0
where λis that the mean of the distribution.

02

Given

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

03

Calculation 

The random variable Xfollows the Poisson distribution with parameter λ(X~P(λ))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 λis very large, this probability can only be calculated using a computer or a calculator).

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