Question

The cars arriving at a gas station is Poisson distributed with a mean of 10 per minute. Determine the number of pumps to be installed if the firm wants to have 50% of arriving cars as zero entries (cars serviced without waiting).

Answer 1

Let N be the number of the cars arriving at a gas station. Then, N ~ Poisson( = 10 per minute)

If the firm wants to have 50% of arriving cars as zero entries, then the number of pumps to be installed equals number of cars arriving with more than 50% probability. Thus,

P(N n) 0.5

Using R, we see that

P(N 9) = 0.4579297

P(N 10) = 0.5830398

Thus, n = 10 is the minimum value for which P(N n) 0.5

Thus, 10 pumps to be installed if the firm wants to have 50% of arriving cars as zero entries.