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

(i)
(a)
Let X be the number of cakes containing fruit, out of 6.

$X ~\sim~ \mathrm{B} (6, 0.4)$

$\mathrm{P} (X = 0) = 0.0467$

(b)
$\mathrm{P} (X \le 2) = 0.544$

(ii)
Let Y be the number of packets with at most 2 cakes containing fruit, out of 8.

$Y ~\sim~ \mathrm{B} (8, 0.54432)$

$\mathrm{P} (Y \ge 4) = 1 - \mathrm{P}(Y \le 3) = 0.729$

(iii)
Let W be the number of packets with at most 2 cakes containing fruit, out of 150.

$W ~\sim~ \mathrm{B}(150, 0.54432)$

Since $n = 150$ is large, $np = 81.648 > 5$ and $nq = 68.352 > 5$,

$W ~\sim~ \mathrm{N}(81.648, 37.20536)$ approximately.

$\mathrm{P}(W > 75) = \mathrm{P}(W > 75.5)$ by continuity correction
$= 0.843$