4. A Geiger counter is observed in the presence of a radioactive source.
In 100 one-minute intervals, the number of counts recorded are as follows:
| No of counts, \(X\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 10 | 24 | 29 | 16 | 12 | 6 | 3 |
- Find the mean and variance of this data, and show that it supports the idea that the random variable \(X\) is following a Poisson distribution.
- Use a Poisson distribution with the mean found in part (a) to calculate, to 3 decimal places, the probability that more than 6 counts will be recorded in any particular minute.
- Find the number of one-minute intervals, in the sample of 100 , in which more than 6 counts would be expected.
\section*{STATISTICS 2 (A) TEST PAPER 10 Page 2}