5 The number of absences per week by workers at a factory has the distribution \(\operatorname { Po } ( 2.1 )\).
- Find the standard deviation of the number of absences per week.
- Find the probability that the number of absences in a 2-week period is at least 2 .
- Find the probability that the number of absences in a 3-week period is more than 4 and less than 8 .
Following a change in working conditions, the management wished to test whether the mean number of absences has decreased. They found that, in a randomly chosen 3-week period, there were exactly 2 absences. - Carry out the test at the \(10 \%\) significance level.
- State, with a reason, which of the errors, Type I or Type II, might have been made in carrying out the test in part (d).