My first post! Anyway I just need a bit of help with a question that I've come across in a textbook which is as follows:
Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. How long can an attendent’s phone call last if the probability is at least .4 that no cars arrive?
Now I just thought this would simply be found by solving for
P(Y=0)≥0.4 with lambda = 4t/3 (working in minutes instead of hours)
So ((4/3)^0).e^-4t/3)/0! ≥0.4
But this is not the answer, and I do not know why it isn’t.