8 Natural background radiation consists of various particles, including neutrons. A detector is used to count the number of neutrons per second at a particular location.
- State the conditions required for a Poisson distribution to be a suitable model for the number of neutrons detected per second.
The number of neutrons detected per second due to background radiation only is modelled by a Poisson distribution with mean 1.1.
- Find the probability that the detector detects
(A) no neutrons in a randomly chosen second,
(B) at least 60 neutrons in a randomly chosen period of 1 minute.
A neutron source is switched on. It emits neutrons which should all be contained in a protective casing. The detector is used to check whether any neutrons have not been contained; these are known as stray neutrons.
If the detector detects more than 8 neutrons in a period of 1 second, an alarm will be triggered in case this high reading is due to stray neutrons. - Suppose that there are no stray neutrons and so the neutrons detected are all due to the background radiation. Find the expected number of times the alarm is triggered in 1000 randomly chosen periods of 1 second.
- Suppose instead that stray neutrons are being produced at a rate of 3.4 per second in addition to the natural background radiation. Find the probability that at least one alarm will be triggered in 10 randomly chosen periods of 1 second. You should assume that all stray neutrons produced are detected.