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

(i)
Let $X =$ number of calls in a period of 4minutes.

$X \sim \text{Po}(4 \times 3) = \text{Po}(12)$

$\text{P}(X=8) = 0.0655$

(ii)
Let $t =$ length of time

Let $Y =$ number of calls in a period of $t$ minutes.

$Y \sim \text{Po}(3t)$

$\text{P}(Y=0) = 0.2$

$e^{-3t} = 0.2$

$t = 0.53648$ minutes
$t = 32$ seconds

(iii)
Let $W =$ number of calls in a working day of 12 hours.

$W \sim \text{Po}(2160)$

Since $\lambda =2160 > 10, W \sim \text{N}(2160, 2160)$ approximately

$\text{P}(W>2200)$

$= \text{P}(W>2200.5)$ by continuity correction

$= 0.192$

(iv)
Let $V =$ number of busy days out of 6 working days.

$V \sim \text{B}(6, 0.19176)$

$\text{P} (V=2) = 0.235$

(v)
Let $U =$ number of busy days out of 30 working days.

$U \sim \text{B}(30, 0.19176)$

Since $n=30$ is large, $np-5.7528 > 5, n(1-p) = 24.2472 >5$

$U \sim \text{N}(5.7528, 4.6496)$ approximately

$\text{P}(U \textless 10)$

$\text{P}(U \textless 9.5)$ by continuity correction

$= 0.959$