FedEx transports packages from Austin to Los Angeles (LA). To get a package from Austin to LA, FedEx takes the package from Austin to Dallas (Route #1), and then from Dallas to LA (Route #2). Group4 graphic.PNG Each route requires a certain amount of travel time for a package. "Travel time" is the amount of time the package is "in motion". Each route experiences delays that occur randomly over time. If a package is in motion when a delay occurs, the delay affects the package, regardless of where the package is along the route. A delay is a "pause" that does not affect travel time. (Imagine that a route is a conveyor belt that pauses when a delay occurs. A pause does not affect the amount of time the conveyor belt must be in motion to get the package from one end to the other, and any pause affects the entire conveyor belt.) The number of delays that a route experiences during an interval of time is random. The "arrival rate" ("occurrence rate") of delays is constant. The numbers of delays in non-overlapping intervals of time are independent. Different routes are independent (each route has its own random process of delays, and each route is unaffected by delays on other routes). Delays on Route #1 occur at an average rate of 0.04 delays per hour. Delays on Route #2 occur at an average rate of 0.045 delays per hour. The route from Austin to Dallas (Route #1) takes 6 hours of travel time. The route from Dallas to LA (Route #2) takes 15 hours of travel time. As stated earlier, "travel time" is the amount of time a package must be "in motion" in order to complete the route. The random variable X1 gives the number of delays a package experiences on the route from Austin to Dallas (Route #1).

The random variable X2 gives the number of delays a package experiences on the route from Dallas to LA (Route #2). What is the expected number of delays a package experiences on Route #2? Three decimals

What is the probability a package will experience zero delays on Route #2? Four decimals

What is the probability a package will experience exactly 1 delay on Route #2? Four decimals

What is the expected number of delays a package will experience going from Austin to LA? Three decimals