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

(i)

Let X denote the mass of food content in a type A packet, in grams

Let Y denote the mass of food content in a type B packet, in grams.

$latex \mathrm{P} (X < 990) = 0.2 $ $latex \mathrm{P} (Z < \frac{990 - 1000}{\sigma}) = 0.2 $ $latex -\frac{10}{\sigma} = -0.84162$ $latex \sigma = 11.8$ (ii) $latex \mathrm{P} (Y < 1000) = 0.314 $ (iii) $latex Y - X ~\sim~ \mathrm{N}(10, 569.18)$ $latex \mathrm{P} (Y > X) = \mathrm{P} (Y – X > 0) = 0.662$

### KS Comments

Students are expected to show the workings for expectation and variance clearly here.