1.Labs that are drawn by providers in a certain hospital are sent to a centralized laboratory through a vacuum system for analysis.Upon arriving to the laboratory, the specimens wait in a collection area until they picked up by a technician for processing.Assume all laboratory specimens have the same priority and are taken from the collection area one at a time by a technician.From historical data, it is known that the arrival of laboratory specimens follows a Poisson distribution with a mean of 37.6 labs per hour.From the same data, the distribution of time between the retrieval of specimens from the collection area was not able to be determined, but the mean time is 1.5 min (i.e. 0.025 hrs or 1:30) and the standard deviation is 0.6 min (i.e. 0.01 hrs or 0:36).

a.What percentage of time will the collection area be empty?

b.How many laboratory specimens would you expect there to be in the collection area at any one time?

c.How long (in minutes) would you expect a laboratory specimen to wait in the collection area before begin retrieved?