Based on extensive data from an urban freeway near Toronto, Canada, “it is assumed that free speeds can best be represented by a normal distribution” [“Impact of Driver Compliance on the Safety and Operational Impacts of Freeway Variable Speed Limit Systems” (J. Transp. Engr. 2011: 260–268)]. The mean and standard deviation reported in the article were 119 km/h and 13.1 km/h, respectively.
a. What is the probability that the speed of a randomly selected vehicle is between 100 and 120 km/h?
b. What speed characterizes the fastest 10% of all speeds?
c. The posted speed limit was 100 km/h. What percentage of vehicles was traveling at speeds exceeding this posted limit?
d. If five vehicles are randomly and independently selected, what is the probability that at least one is not exceeding the posted speed limit?
e. What is the probability that the speed of a randomly selected vehicle exceeds 70 miles per hour?