Customers arrive at the service window in their car from a bank according to a Poisson distribution, a time study was performed in the past month with the following observations:

	week 1	week 2	week 3	week 4
number of observations	5400	6850	4320	7225
Arrival of Customers per hour ()	16.60	18.80	17.50	1860

Perform an average weight of customer input based on these information, consider two significant figures after the point. As for the Service time per customer is exponential with a mean of 3 minutes. There are three spaces in front of the window, including the car being serviced. other cars Arriving drivers line up outside this 3-car space.

a) What is the probability that an arriving car can enter one of the 3 spaces?

b) What is the probability that an arriving car waits outside the space designated for three 3 cars?

c) How long is an arriving customer expected to wait before starting the service? service and how many customers on average would be waiting in line?

d) How many spaces for cars should be provided in front of the window (including the one being serviced) so that an arriving car can find a space there at least 89% of the time?

e) For 90% of the customers who arrive at the window, it is desired that the time of wait does not exceed 30 minutes, the system meets this criteria.