The AlphaCor Company experiences some type of failure on its computer network on average once every 4 hours. Assume that each failure is independent of all other failures and no two failures occur at the same time.
a) Let F be the number of failures on the network during one 24 hour day. State the distribution and parameter(s) of F.
b) What is the probability that there are between 5 and 7 network failures inclusive in the next 24 hours?
c) What is the probability that there were 3 failures between 1:00 pm and 10:00 pm and there were no failures from 10:00 pm to midnight?
d) Let T be the time in hours until the next failure occurs. State the distribution and parameter(s) of T.
e) What is the probability that it takes between 1.5 and 4 hours until the next network failure?
f) The day shift IT supervisor comes in and notices that the log listing the network failures shows
3 failures between Midnight and 8:00 am, but the times of the failures were not recorded. What is the probability that at least 1 of the failures occurred between 2:00 am and 3:00 am?