All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
The mean number of absences per day is constant.

(ii)

Let A be the number of absentees from Admin Department on n days.

$A~\sim~\mathrm{Po}(1.2n)$

$latex \mathrm{P}(A=0) = e^{-1.2n} < 0.01$ $latex n > 3.8$

$\therefore, \mathrm{smallest~number~of~days} = 4$

(iii)

Let T be the number of absentees from two Departments on 5 days.

$T~\sim~\mathrm{Po}(19.5)$

$\mathrm{P}(T>20) = 1- \mathrm{P}(T \le 20) = 0.397$

(iv)

Let S be the number of absentees from two Departments on 60 days.

$S~\sim~\mathrm{Po}(234)$

Since $\lambda = 234 > 10, S ~\sim~N(234, 234)$ approximately.

$\mathrm{P}(200 \le S \le 250) = \mathrm{P}(199.5 \le S \le 250.5) = 0.848$