The reference desk of a university library receives request for assistance. assume that a poisson probability distribution with an arrival rate of 10 request per hour can be used to describe the arrival pattern and that service time follow an exponential probability distribution with a service rate of 12 request per hour.

a. what is the probability that no requests for assistance are in the system?
b. what is the average number of requests that will be waiting for service?
c. what is the average time in minutes before service begins?
d. what is the average time at the reference desk in minutes (waiting time plus service time)?
e. what is the probability that a new arrival has to wait for service?

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.