Suppose your wait time for a shuttle bus in the morning is normally distributed with µ=8 minutes and t1=5 minutes. Due to increased congestion in the afternoon, your wait time for a shuttle bus in the afternoon is normally distributed with µ=10 minutes and t2=8 minutes.
A. If you take the bus each morning and afternoon for a week (Monday through Friday), what is your total expected waiting time? [Hint: Define random variables X1, ..., X10 and use a rule of expected value.)
B. What is the standard deviation of your total weekly waiting time?
C. If individual bus arrival times are independent of other buses, what is the probability that your weekly total bus waiting time is less than 1 hour?
D. What are the expected value and standard deviation of the difference between morning and evening waiting times on any single day?
E. What are the expected value and standard deviation of the difference between total morning waiting time and total evening waiting time for a particular week?