Question

To save on gasoline expenses, Edith and Mathew agreed to carpool together for traveling to and from work. Edith preferred to travel on I-20 highway as it was usually the fastest, taking 25 minutes in the absence of traffic delays. Mathew pointed out that traffic jams on the highway can lead to long delays making the trip 45 minutes. He preferred to travel along Shea Boulevard, which was longer (35 minutes), but rarely had traffic jams. Edith agreed that in case of traffic jams, Shea Boulevard was a reasonable alternative. Neither of them knows the state of the highway ahead of time. After driving to work on the I-20 highway for 1 month (20 workdays), they found the highway to be jammed 3 times. Assuming that this month is a good representation of all months ahead, should Edith and Mathew continue to use the highway for traveling to work?

How would you conclusion change for the winter months, if bad weather makes it likely for traffic jams on the highway to increase to 6 days per month?

How would your conclusion change if Mathew purchased a new smart-phone app that could show the status of the highway traffic prior to their drive each morning, thus reducing the probability of them getting into a jam down to only 1day per month (where on this day, the app showed no traffic jam, but a jam developed in the meantime as they were driving along the highway).

Answer 1

Answer:

(a) Probability of I-20 to be jammed in a month = 3/20 = 15% Expected time along 1-20 = 25 minutes x 85% + 45 minutes x 15%= (21.25 +6.75) minutes = 28 minutes Expected time along Boulevard = 35 minutes Since Highway takes less expected time, highway is the better option. (6) Probability of I-20 to be jammed in a month = 6/20 = 30% Expected time along 1-20 = 25 minutes x 70% +45 minutes x 30%= (17.5+ 13.5) minutes = 31 minutes Expected time along Boulevard = 35 minutes Since Highway takes less expected time, highway is the better option.