(4) Suppose that number of visits to an international travel website can described by a Poisson model (process) with a rate of 5 per minute during the business hours.

(a) What is the probability that there will be more than 85 visits to the website during 9:00 am - 9:20 am period ? What is the expected number of visits during 1:30 pm-2:00 pm ?

(b) What is the expected time between two visits to the site ? What is the probability that the time between two visits to the site is less than 30 seconds ?

(c) What is the joint probability of having more than 70 visits to the site between 1:00 pm-1:15 pm and less than 90 visits between 2:00 pm-2:20 pm ?

(d) What is the expected time until the fourth visit to the site anytime during business hours ?