7 The number of workers, \(X\), absent from a factory on a particular day has the distribution \(\mathrm { B } ( 80,0.01 )\).
- Explain why it is appropriate to use a Poisson distribution as an approximating distribution for \(X\).
- Use the Poisson distribution to find the probability that the number of workers absent during 12 randomly chosen days is more than 2 and less than 6 .
Following a change in working conditions, the management wishes to test whether the mean number of workers absent per day has decreased.
- During 10 randomly chosen days, there were a total of 2 workers absent. Use the Poisson distribution to carry out the test at the \(2 \%\) significance level.