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Use the following information to answer the next six exercises: On average, a clothing store gets120 customers per day.

What is the probability that the store will have fewer than 12customers in the first two hours?

Short Answer

Expert verified

The probability of getting smaller than 12guests in the first two hours at the store i.e.,P(Y<12)is 0.0214

Step by step solution

01

:Given 

Number of guests per day=120
Number of opening hours per day =12
Let us define a arbitrary variableY as
Y=number of guests arriving in the first two hours at the apparel store.Y follows a Poisson distribution
Formulaused
The probability ofysuccesses is the given as
localid="1648544017477" P(Y=y)=e-λλyy!=;y=0,1,2,3,......&λ>0

02

Calculation

Number of guests per hour=120/12=10
Number of guests per two hours=10*2=20
Thus, in this caseλ=average number of guests per two hours=20i.e.,Y~P(20).
We want to find the probability of getting smaller than 12 guests in the first two hours i.e.,P(Y<12). This can be attained as
P(Y<12)=P(Y=0)+P(Y=1)+P(Y=2)+.....+P(Y=11)
=y=011e-λλyy!=0.0214

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