Tim gets 15 emails on average per day (i.e. per 24 hours). Emails arrive randomly and independently.
a) What is probability that Tim gets exactly 12 emails on a particular day?
b) Find the probability that he gets at least 3 emails on a particular day?
c) What is the standard deviation of the number of emails that Tim gets in one day?
d) In one hour, given that Tim received at least one email, what is the probability that he received less than 3 emails (in that same hour)?
e) What is the probability that Tim gets 4 emails between 2:00 pm and 5:00 pm and then 2 emails between 6:00 pm and 8:00 pm in the same day?
f) What is the expected number of emails that Tim gets in a week?