s we all know, no one comes on time for a class scheduled at 8:30 AM. Fed up with this, theinstructor decided that there is a uniform probability that the doors will be closed sometimebetween 8:30 AM and 8:45 AM. If students always come to class late and as a poisssonprocess with rate λ, what is the expected number of people who will get attendance?

Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take, on average, 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. a. What percentage of time is Judy idle? (Round your answer to 1 decimal place.)

Shuttle bus which links the Clayton campus to the Caulfied campus starts operating at 5:00 am and will have a service every half hour. Suppose that none of the seats on the bus are completely occupied and that there is always some room for passengers. A student who wants to travel to Caulfied arrives at the bus stop at a (uniform) random time between 8:45 am and 9:45 am. What is the probability that he/she waits at most 10 minutes? Write down your answer to an accuracy of 2 decimal points.

A Discrete Mathematics professor has a class of students. Frustrated with their lack of discipline, the professor decides to cancel class if fewer than some number of students are present when class starts. Arrival times go from on time () to arrived late ().Given the arrival time of each student and a threshhold number of attendees, determine if the class is cancelled.ExampleThe first students arrived on. The last were late. The threshold is students, so class will go on. Return YES.Note: Non-positive arrival times () indicate the student arrived early or on time; positive arrival times () indicate the student arrived minutes late.Function DescriptionComplete the angryProfessor function in the editor below. It must return YES if class is cancelled, or NO otherwise.angryProfessor has the following parameter(s):int k: the threshold number of studentsint a[n]: the arrival times of the studentsReturnsstring: either YES or NOInput FormatThe first line of input contains , the number of test cases.Each test case consists of two lines.The first line has two space-separated integers, and , the number of students (size of ) and the cancellation threshold.The second line contains space-separated integers () that describe the arrival times for each student.ConstraintsSample Input24 3-1 -3 4 24 20 -1 2 1Sample OutputYESNOExplanationFor the first test case, . The professor wants at least students in attendance, but only have arrived on time ( and ) so the class is cancelled.For the second test case, . The professor wants at least students in attendance, and there are who arrived on time ( and ). The class is not cancelled.

For a small batch computing system the processing time per job is exponentiallydistributed with an average time of 3 minutes. Jobs arrive randomly at an average rateof one job every 4 minutes and are processed on a first-come-first-served basis. Themanager of the installation has the following concerns.(a) What is the probability that an arriving job will require more than 20 minutes to beprocessed (the job turn-around time exceeds 20 minutes)?(b) A queue of jobs waiting to be processed will form, occasionally. What is the averagenumber of jobs waiting in this queue?

Students arrive at Central Library at an average of 15 per quarter of the lunch hour. What is the probability that the next student will arrive within 5 minutes? ( round your answer to four decimal places)