(a)[5]
Calculate the probability that the combined mass of the box and its contents is greater than $500$ grams.
(b)[5]
Calculate the probability that the mass of seeds in the box is smaller than $1.4$ times the mass of raisins in the box.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
A box of Seeds & Raisins has $S$ grams of seeds and $R$ grams of raisins. When the box is empty, its mass is $B$ grams. $S$, $R$ and $B$ are independent random variables, with $S \sim N(300, 45)$, $R \sim N(200, 25)$ and $B \sim N(15, 4)$. One complete box of Seeds & Raisins is picked at random.