4 A radioactive source contains 1000000 nuclei of a particular radioisotope. On average 1 in 200000 of these nuclei will decay in a period of 1 second. The random variable \(X\) represents the number of nuclei which decay in a period of 1 second. You should assume that nuclei decay randomly and independently of each other.
- Explain why you could use either a binomial distribution or a Poisson distribution to model the distribution of \(X\).
Use a Poisson distribution to answer parts (b) and (c).
- Calculate each of the following probabilities.
- \(\mathrm { P } ( X = 6 )\)
- \(\mathrm { P } ( X > 6 )\)
- Determine an estimate of the probability that at least 60 nuclei decay in a period of 10 seconds.