Poisson Process

[dalekissell]

Hello I really need help with this problem and I have to show my work. We went over the Poisson equation but I can't figure out how to plug everything in to get a %.

The number of hits to a website follows a Poisson process and occurs at the rate of 10 calls per minute between 7pm and 9 pm. How long should you expect to wait before the probability of at least 1 hit to the site is 95%.

Thank you in advance for the help.

[BGM]

Note the possion process N(t) ~ Possion(10t), where t is the number of minutes we wait
Therefore Pr{N(t) ≥ 1} > 95%
⇒ 1 - Pr{N(t) = 0} > 0.95
⇒ e^(-10t) < 0.05
⇒ -10t < ln(0.05)
⇒ t > -ln(0.05)/10 = 0.29957322735539909934352235761425 minutes
(or 17.974393641323945960611341456855 seconds)