A company is preparing to launch a new web site to sell its products. From past experience, they know that purchases at the site will occur as a Poisson process with on average 22 purchases every 10 minutes.

1. (1 pts) 1 What is the expected time in minutes before the first purchase after the site opens? Give your answer to four decimal places. Response:

2. (1 pts) 1 What is the probability that more than 0.16 minutes pass before the first purchase? Give your answer to four decimal places. Response:

3. (1 pts) 1 What is the expected time in minutes until the sixth purchase? Give your answer to four decimal places. Response:

4. (1 pts) 0 What is the probability that the sixth purchase will occur between 2.27 minutes and 3.18 minutes after the site opens? Give your answer to four decimal places. Response: