Related questions with answers
When making a connection at an airport, Jasmine arrives on a plane that is due to arrive at 2:15 P.M. However, the amount by which her plane arrives late has a normal distribution with a mean minutes and a standard deviation minutes. Jasmine wants to transfer to a plane that is due to depart at 3:25 P.M., although the actual departure time is late by an amount that is normally distributed with a mean minutes and a standard deviation minutes. If Jasmine needs 30 minutes at the airport to get from the arrival gate to the departure gate, what is the probability that she will be able to make her connection?
Let represents the amount (in minutes) by which Jasmine's plane arrives late and represents the amount (in minutes) of departure time late. It is given that
These times are independent. Using the general result about linear combinations of independent normal random variables, we get:
Furthermore, let be the amount of time (in minutes) measured after 2:00 P.M. to arrival gate, and let be the amount of time (in minutes) measured after 2:00 P.M. to departure gate.
This is illustrated in Figure1, from where we can see that
Notice that Jasmine will be able to make her connection iff
Therefore, the requared probability is
Recommended textbook solutions
More related questions