A New Shopping Mall Is Considering Setting Up an Information

question 59

Essay

A new shopping mall is considering setting up an information desk operated by two employees.Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour.It takes an average of 4 minutes to answer a question.It is assumed that arrivals are Poisson and answer times are exponentially distributed.
(a)Find the proportion of the time that the employees are busy.
(b)Find the average number of people waiting in line to get some information.
(c)Find the expected time a person spends just waiting in line to have his question answered.

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Definitions:

Draw

A term referring to either a poker game variant, the process of selecting something in a random manner, such as in a lottery, or drawing funds against a line of credit.

Responsible

Being accountable for something within one's power, control, or management.

Service Fee

A charge levied for the provision of a particular service, often added to the basic cost of the service.

Dishonors

Refers to the failure to fulfill an obligation or agreement, especially in the context of finance, like a cheque not being paid due to insufficient funds.