A sample of radioactive material decays randomly, with an approximate mean of 1.5 counts per minute.
Name a distribution that would be suitable for modelling the number of counts per minute.
Give any parameters required for the model.
Find the probability of at least 4 counts in a randomly chosen minute.
Find the probability of 3 counts or fewer in a random interval lasting 5 minutes.
More careful measurements, over 50 one-minute intervals, give the following data for \(x\), the number of counts per minute:
$$\sum x = 84 , \quad \sum x ^ { 2 } = 226$$
Decide whether these data support your answer to part (a).
Use the improved data to find probability of exactly two counts in a given one-minute interval.