The time it takes Alice to walk to the bus stop from her home is Normally distributed with mean 11 minutes and variance 2 minutes$^2$. The waiting time for the bus to arrive is Normally distributed with mean 5 minutes and standard deviation 2 minutes. Her bus journey to the UBC bus loop is a Normal variable with mean 24 and standard deviation 5 minutes. The time it take Alice to walk from the bus loop to the lecture theatre to attend STAT 251 is Normally distributed with mean 18 minutes and variance 4 minutes$^2$. The total time taken for Alice to travel from her home to her STAT 251 lecture is Normally distributed. Please use R to find probabilities.

Part a) What is the mean travel time (in minutes)?

Part b) What is the standard deviation of Alice's travel time (in minutes, to 2 decimal places)?

Part c) The STAT 251 class starts at 8 am sharp. Alice leaves home at 7 am. What is the probability (to 2 decimal places) that Alice will not be late for her class?