Draw a diagram that shows this information.

(i)     Find the probability that a box of cereal, chosen at random, is sold.

(ii)     Calculate the manufacturer’s expected daily income from these sales.

Calculate the manufacturer’s expected daily recycling cost.

Calculate the value of $w$.

(A1)(A1)

Notes:     Award (A1) for bell shape with mean of 502.

Award (A1) for an indication of standard deviation eg 500 and 504.

[2 marks]

(i)     $0.921{\text{ }}(0.920968 \ldots ,{\text{ }}92.0968 \ldots \% )$     (G2)

Note:     Award (M1) for a diagram showing the correct shaded region.

(ii)     $1500 \times 2 \times 0.920968 \ldots$     (M1)

$= {\text{ }}(\$ ){\text{ }}2760{\text{ }}(2762.90 \ldots )$    (A1)(ft)(G2)

Note:     Follow through from their answer to part (b)(i).

[4 marks]

$1500 \times 0.16 \times 0.079031 \ldots$    (M1)

Notes:     Award (A1) for $1500 \times 0.16 \times {\text{ their }}(1 - 0.920968 \ldots )$.

OR

$(1500 - 1381.45) \times 0.16$    (M1)

Notes:     Award (M1) for $(1500 - {\text{their }}1381.45) \times 0.16$.

$= (\$ )19.0{\text{ (}}18.9676 \ldots )$    (A1)(ft)(G2)

[2 marks]

$347{\text{ }}({\text{grams}}){\text{ }}(346.614 \ldots )$    (G3)

Notes:     Award (G2) for an answer that rounds to 346.

Award (G1) for $353.385 \ldots$ seen without working (for finding the top 3%).

[3 marks]