Consider an espresso stand with a single barista. customers arrive at the stand at the rate of 28 per hour according to a poisson distribution. service times are exponentially distributed with a service rate of 35 customers per hour. the probability that the server is busy is:

The probability that the server is busy is P=0.56.

Step-by-step explanation:

We have a quieing theory problem with M/M/1

In queing theory, the probability of the server being busy can be expressed as:

being μ: the time between services and λ: the time between customers arrival.

Then we can calculate:

The probability that the server is busy is P=0.56.

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8