At the start of football season, the ticket office gets very busy the day before the first game. customers arrive at the rate of four every 10 minutes, and the average time to transact business is 2 minutes. the average number of people in line is customers (round your response to one decimal place). the average time that a person will spend at the ticket office is minutes (enter your response as a whole number). the proportion of time that the server is busy is (round your response to one decimal place).

(a) 3.2

(b) 10 minutes

(c) 0.8

Explanation:

Mean number of customer in service:

= Arrival rate ÷ service rate

= 24 in 60 min ÷ 30 in 60 min

= 24 ÷ 30

= 0.8

a) Average number of people in line:

= (Mean number of customer in service × arrival rate) ÷ (Service rate - arrival rate)

= 0.8 × (24 ÷ 6 )

= 3.2

b) Average time spend at the ticket office is = 10 minutes

c) Proportion of time server is busy:

= Arrival rate ÷  service rate

= (24 in 60 min ÷  30 in 60 min)

= 24 ÷ 30

= 0.8

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