2 Jess is watching a shower of meteors (shooting stars). During the shower, she sees meteors at an average rate of 1.3 per minute.
- State conditions required for a Poisson distribution to be a suitable model for the number of meteors which Jess sees during a randomly selected minute.
You may assume that these conditions are satisfied.
- Find the probability that, during one minute, Jess sees
(A) exactly one meteor,
(B) at least 4 meteors. - Find the probability that, in a period of 10 minutes, Jess sees exactly 10 meteors.
- Use a suitable approximating distribution to find the probability that Jess sees a total of at least 100 meteors during a period of one hour.
- Jess watches the shower for \(t\) minutes. She wishes to be at least \(99 \%\) certain that she will see one or more meteors. Find the smallest possible integer value of \(t\).