Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow. So, getting stopped by a train will likely make you late for work. You start recording data to determine the likelihood of arriving at the tracks while a train is there. Open data set 5_1_37 at www.pearsonhighered.com/ sullivanstats, which contains the day number and whether a train was present, or not, for 200 consecutive days in which you drove to work. The column “Train” shows a series of 0s and 1s. In that column, a 0 indicates there was no train present and a 1 indicates that a train was present. The column “Aggregate Train” represents the cumulative number of times a train was present. The column “Aggregate Proportion Train” represents the cumulative proportion of times a train was present.
(a) Explain why getting stuck by the train is a random process.
(b) What proportion of the days was a train present after 8 days?
(c) What proportion of the days was a train present after 20 days?
(d) Were you stopped by a train on the 30th day?
(e) Graph the proportion of days a train was present against the number days (the number of days should be on the horizontal axis).
(f) What is the estimate of the probability of being struck by a train during your commute?