In: Statistics and Probability
The Department of Engineering at NJIT conducted a study on the average number of trains passing through the Hoboken train station. The study showed that the average is six per hour and that the passing of these trains is approximated by the Poisson distribution. (a) Find the probability that no trains passed through the Hoboken train station between 8am and 9.0am on Tuesday. (b) Find the probability that exactly four trains passed during that time. (c) Find the probability that exactly six trains passed during that time. (d) Find the probability that ten or more trains passed during that time. Please show all work.