4MA0 Foundation January 2014 Paper 1 Q16
16 A box contains 80 tea bags.
The table shows information about the weight of each tea bag.
| Weight (\(w\) grams) | Number of tea bags |
|---|---|
| \(2.8 \lt w \leqslant 2.9\) | 2 |
| \(2.9 \lt w \leqslant 3.0\) | 4 |
| \(3.0 \lt w \leqslant 3.1\) | 22 |
| \(3.1 \lt w \leqslant 3.2\) | 32 |
| \(3.2 \lt w \leqslant 3.3\) | 14 |
| \(3.3 \lt w \leqslant 3.4\) | 6 |
(a) Work out the percentage of the 80 tea bags that weigh more than 3.1 grams. (2)
(b) Work out an estimate for the total weight of the 80 tea bags.
Use halfway values of 2.85 grams, 2.95 grams, ... (3)
Use halfway values of 2.85 grams, 2.95 grams, ... (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{32 + 14 + 6}{80} \times 100\) oe | M1 |
| 65 | A1 |
| (2) |
Notes
M1: for \(\dfrac{32 + 14 + 6}{80}\) or 0.65
A1: cao
| Scheme | Marks |
|---|---|
| 2.85 × 2 + 2.95 × 4 + 3.05 × 22 + 3.15 × 32 + 3.25 × 14 + 3.35 × 6 or 5.7 + 11.8 + 67.1 + 100.8 + 45.5 + 20.1 | M1 |
| M1 | |
| 251 | A1 |
| (3) | |
| (Total 5 marks) |
Notes
M1: for at least two products \(f \times x\) consistently within intervals (inc end points)
M1: for complete correct method (condone any one error)
NB. products do not need to be evaluated
A1: cao