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

(i)
$Y -2X \sim \text{N}(40, 7400)$

$\text{P} (Y>2X)$

$= \text{P} (Y-2X>0)$

$= 0.681$

(ii)
$0.05Y + 0.12X \sim \text{N}(41.6, 21.96)$

$\text{P} (0.05Y + 0.12X > 45)$

$= 0.234$

(iii)
Let $X_1, X_2 =$ number of peak rate calls over the two three-month periods.

$0.12(X_1+X_2) \sim \text{N} (43.2, 25.92)$

$\text{P}(0.12(X_1+X_2) > 45)$

$= 0.362$