A website gets four hits every ten minutes, on average. Use a Poisson process to model the number of hits. (a) How many hits does the website get per hour, on average? (b) What is the chance the website will get exactly 20 hits during the next hour? (Use the Poisson probability mass function.) (c) What is the chance the website will get 20 or more hits during the next hour? (You may want to use the Poisson cumulative probability table in the textbook.) (d) Can you determine the expected time between hits? (The average amount of time between arrivals.) (e) What is the chance that 5 or more minutes pass between two hits? (Use one of the Exponential formulas.) (f) Suppose the website begins to receive advertising revenue after 25,000 hits. The amount of time, in minutes, until 25,000 hits is Gamma with α=25,000 and λ=4/10. Find the average amount of time until the 25,000th hit in minutes, then convert to days. (g) The amount of time in minutes that will pass before the website receives another 30 hits is Gamma with α=30 and λ=4/10. What is the chance that 60 or more minutes pass before another 30 hits? (Use the Gamma-Poisson formula. )
