(a)[1]
Determine the standard deviation for the weekly number of absences.
(b)[3]
Find the probability that the number of absences over a 2-week period is at least $2$.
(c)[2]
Find the probability that the number of absences in a 3-week period is greater than $4$ but less than $8$.
(d)[5]
After a change in working conditions, management wanted to check whether the mean number of absences has fallen. They discovered that, in a randomly selected 3-week period, there were exactly $2$ absences. Carry out the test at the $10\%$ significance level.
(e)[2]
State, giving a reason, which error, Type I or Type II, could have occurred when carrying out the test in part (d).