1. The vehicle dispatching decisions of an airport-based taxi service were investigated. In modeling the system, the authors assumed travel times of successive trips to be independent exponential variables. Assume ?= 0.05.
a. What is the mean trip time for the taxi service?
b. What is the probability that a particular trip will take more than 30 minutes?
c. Two taxis have just been dispatched. What is the probability that both will be gone for more than 30 minutes? That at least one of the taxis will return within 30 minutes?
2. The National Collegiate Athletic Association (NCAA) requires Division I athletes to score at least 820 on the combined Mathematics and Verbal parts of the SAT to compete in their first college year. (Higher scores are required for students with poor high school grades.) In 2000, the scores of the 1,260,000 students taking the SATs were approximately Normal with mean 1019 and standard deviation 209. What percent of all students had scores less than 820?