You have two different subway lines that you can take to NYU each day. The R train takes 30 minutes on average and has a standard deviation of 6 minutes. The 6 train takes 32 minutes and has a standard deviation of 5 minutes. The number of minutes it takes on both subway lines is normally distributed, and for the purposes of this problem assume that the R and 6 train travel times are independent random variables.

(a) What is the probability that on a given day, taking the 6 train will be faster than taking the R train?

(b) What is the probability that taking the 6 train for two weeks (10 trips) would give you a lower average time than taking the R train for those two weeks?

(c) You need to get to campus in 45 minutes or less to arrive on time for a job interview. Which train will maximize the probability you get there on time?