(a)[1]
Determine the standard deviation for the number of absences per week.
(b)[3]
Find the probability that the number of absences in a 2-week interval is at least $2$.
(c)[2]
Find the probability that, in a 3-week period, the number of absences is more than $4$ and less than $8$.
(d)[5]
After a change in working conditions, management wanted to test whether the mean number of absences has decreased. In a randomly selected 3-week period, they recorded exactly $2$ absences. Carry out the test at the $10\%$ significance level.
(e)[2]
State, with a reason, which error, Type I or Type II, could have occurred when carrying out the test in part (d).