The number of emails a professor receives per day is observed to be a Poisson random variable with a variance of 81. The professor replies to each email with a probability of 2/3, independently of all other emails, and each reply takes five minutes to write. What is the expected length of time spent writing email replies per day (to the nearest minute)?
Select one:
a. None of the other choices
b. 30 minutes
c. 37 minutes
d. 405 minutes
e. 270 minutes