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In: Statistics and Probability

At an inside sales counter an average of 20 customers enter the system for service each...

At an inside sales counter an average of 20 customers enter the system for service each hour, it takes about five minutes to serve each customer. The manager has been staffing the counter with three sales associates. She wonders if she should reduce the staffing level to two. What is the probability that more than two people enter the system in a five-minute period? What about more than 4?

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Expert Solution

ANSWER::

expected number of customer in 5 minute =20*5/60=5/3

a)

P(more than two people enter the system in a five minute period)=P(X>2) =1-P(X=0)-P(x=1)-P(X=2)

=1-e-5/3*(5/3)0/0!-e-5/3*(5/3)1/1!-e-5/3*(5/3)2/2!=0.2340

b)

P(more than four people enter the system in a five minute period)=P(X>4) =1-P(X=0)-P(x=1)-P(X=2)-P(X=3)-P(X=4)

=1-e-5/3*(5/3)0/0!-e-5/3*(5/3)1/1!-e-5/3*(5/3)2/2!-e-5/3*(5/3)3/3!-e-5/3*(5/3)4/4!= 0.0275

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orchestra answered 2 years ago
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