Hello please answer this question I need your own work. Pease typing not HAND wr

Question

Hello please answer this question I need your own work.

Pease typing not HAND writing

A gas station with only one gas pump employs the following policy: If a customer has to wait, the price is $3 per gallon; if she does not have to wait, the price is $3.50 per gallon. Customers arrive according to a Poisson process with a mean rate of 30 per hour. Service times at the pump have an exponential distribution with a mean of 1.5 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the expected price of gasoline per gallon.

Explanation / Answer

Solution:

Let x be the average no of arrivals per unit of time 30 per hour
Let y be the service rate = 24 per hour
Probability of more than 1 car in the system = (x/y)(1+1) = (30/24)2 = 1.56%
So probability of 1 or less car is 60%
So the average rate = 0.66*3.50 + 1.56*3.0 = $6.99

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