Problem 1

John can take either of two routes to IAH airport from his home (Route A or Route B). Owing to varying traffic conditions the travel times for the two routes are not fixed, rather on a Friday around midday the travel times across these routes can be well approximated per normal distributions as follows,

Route A: m_A =54 minutes, s_A = 6 minutes

Route B: m_B =60 minutes, s_B = 3 minutes

(a) Which route should he choose if on midday Friday he must be at the airport within 54 minutes to pick up his spouse? Briefly explain your answer.

(b) Which route should he choose if on midday Friday he must be at the airport within 60 minutes to pick up his spouse? Briefly explain your answer.

(c) Which route should he choose if on midday Friday he must be at the airport within 66 minutes to pick up his spouse? Briefly explain your answer.

(d) This past year John has been regularly driving from his home to IAH on Fridays (midday) to pick up his spouse who is a contract consultant and has to travel out of Houston on contract jobs. 30% of these trips he has used route A to reach IAH and 70% of the trips he has used route B.

Out of the 48 Fridays that he picked up his spouse from IAH this past year, how many days would you expect he was able to reach IAH within 60 minutes? Please provide calculations to support your answer.