Refer to the "Cars at an intersection" example in Section 4.1.1 to answer the questions below.
(a) The data for this problem were collected between 3:25p.m. and 4:05p.m. on a non-holiday weekday. Ideally, it would also be important to understand the traffic patterns for other time periods. The number of cars stopped at the intersection is likely to vary due to factors such as time of day, day of the week, whether school is in session, and so forth. Discuss how these factors could have been accounted for in designing this study.
(b) Are the observations truly independent? If not, discuss what assumptions must be made to use the Poisson distribution for this problem.
(c) The lengths of vehicles and the distances between stopped vehicles vary. For the purpose of this problem, suppose all vehicles are 14 feet long with a distance between cars of 4 feet when stopped at the intersection. This suggests that 9 vehicles (150/18 = 8.3) or more will at least partially block the fire station's driveway. Using a Poisson distribution, estimate the probability this will happen for one stoplight cycle. Considering part (a), what caveats need to be placed on the interpretation of this probability?
(d) Using the probability from part (c), estimate the probability that the fire station's driveway is at least partially blocked at least once over 60 cycles of the light (roughly one hour). Use the binomial distribution to help answer this problem.