Date | November 2016 | Marks available | 2 | Reference code | 16N.2.SL.TZ0.T_4 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Calculate | Question number | T_4 | Adapted from | N/A |
Question
A manufacturer produces 1500 boxes of breakfast cereal every day.
The weights of these boxes are normally distributed with a mean of 502 grams and a standard deviation of 2 grams.
All boxes of cereal with a weight between 497.5 grams and 505 grams are sold. The manufacturer’s income from the sale of each box of cereal is $2.00.
The manufacturer recycles any box of cereal with a weight not between 497.5 grams and 505 grams. The manufacturer’s recycling cost is $0.16 per box.
A different manufacturer produces boxes of cereal with weights that are normally distributed with a mean of 350 grams and a standard deviation of 1.8 grams.
This manufacturer sells all boxes of cereal that are above a minimum weight, .
They sell 97% of the cereal boxes produced.
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 .
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
(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) (G2)
Note: Award (M1) for a diagram showing the correct shaded region.
(ii) (M1)
(A1)(ft)(G2)
Note: Follow through from their answer to part (b)(i).
[4 marks]
(M1)
Notes: Award (A1) for .
OR
(M1)
Notes: Award (M1) for .
(A1)(ft)(G2)
[2 marks]
(G3)
Notes: Award (G2) for an answer that rounds to 346.
Award (G1) for seen without working (for finding the top 3%).
[3 marks]