Purdue students are able to connect with Itap server to use some software remotely on their own computer. Assume that for each time a student utilizes the software remote service he/she uses it for an average of 35 minutes. Let T denote the time that a student uses the software remote in a single session.
a) Name the distribution and specify the parameters of T.
b) What's the probability that in session with the software remote, student uses it for more than 45 min?
c) Given that the student does not finish his/her session on the software remote in 40 min, what's the probability he/she will use the software remote service for more than 70 min?
d) Itap has decided to limit the maximum time a student uses the remote service per session. However, they have to ensure that at least 90% of the students can finish their computing job on the software remote. What should Itap use as cutoff for the maximum time so that at least 90% of student users complete their computing job? (give both exact answer and then round up to the nearest minute)