Question

The average number of customers at a window of a certain bank per minute during banking hours is four. Find the probability that during a given minute. i. No customers appear ii. Three or fewer customers

Answer 1

we are given mean=4

This problem is based on exponential distribution:

X=no of customers appear

X~exp(0.25)

P(X=x)=

(A)

P(no customers appear)=P(X=0)=

P(X=0)=

P(X=0)=

P(X=0)=0.25

P(no customers appear)=P(X=0)=0.25

(B)P(3 or fewer customers arrive)=P(X 3)

P(X 3)=

P(X 3)=

P(X 3)=0.25

P(X 3)=

P(X 3)=

P(X 3)=

P(X 3)=

P(X 3)=

P(X 3)=0.527633

P(3 or fewer customers arrive)=P(X 3)=0.527633

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