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BSCI 1510L Literature and Stats Guide: 5.1 Aside: Commuting to Nashville

Introduction to Biological Sciences lab, first semester

5.1 Aside: Commuting to Nashville

An important question facing all commuters is "how long will it take me to get to work?"  I know from years of experience that if I leave home at 6:45 AM, on average I will arrive at the parking garage at 7:30 AM.  However, on any given day, I rarely arrive at exactly 7:30.  Why?  Sometimes I have bad luck and hit a lot of red lights in town.  Sometimes I have good luck and there is no traffic backed up on the Interstate anywhere on my route.  On a typical day, a random factor that happens to slow me down (a particular red light, a particular spot on the Interstate where traffic is slow, bad weather) is balanced out by some other factor that allows me to go faster (a particular green light, no people pulled over for speeding or accidents, good weather) and I get to work about 7:30, plus or minus about 5 minutes.  About once a week, I have worse than average luck (all the lights are red, there are several places along my route where there are accidents) and I am more than 10 minutes later than 7:30.  Every couple months I have really bad luck with many factors working against me I'm more than a half hour late.  Once every year or two, there is a hazardous waste truck that's turned over and the Interstate is shut down, or there is an ice storm and cars are driving 20 miles per hour, or some other improbable sequence of events happens that makes me more than an hour late. 

So if you asked me how long it takes me to commute to work, the best answer would be to express it with reference to probabilities rather than giving a single value.  My mean travel time to work is 45 minutes, but about 40% of the time, my actual commuting time differs by 45 minutes by more than 5 minutes.  About 15% of the time, my actual commuting time differs by more than 10 minutes.  About 5% of the time, my actual commuting time differs from the mean by more than a half hour.  Less than 1% of the time my actual commuting time is longer than an hour.  So I can describe the variation in my commuting time by relating it to the probability of having bad luck and having many random factors working against me at once. 

Now, let's say that I have a very important meeting at 7:30 AM.  When should I leave home to make sure that I'm not late to the meeting?  Well, there is no particular time that I can leave and be 100% certain that I will get to the meeting on time.  No matter what time I choose to leave, there will be some probability that I will be late.  So I will choose a leaving time that reduces the probability of being late to an acceptable level, e.g. if I leave at 6:15 AM (allowing an extra half hour) there is less than a 5 % chance I will be late.  If I want to be more sure than that about being on time, I will have to leave earlier.