Higher January 2023 Paper 2 Q18
18 The table gives information about the weights, in kg, of the parcels that Pedro delivers on Monday.
| Weight (\(w\) kg) | Frequency |
|---|---|
| \(0 \lt w \leqslant 2\) | 12 |
| \(2 \lt w \leqslant 3\) | 7 |
| \(3 \lt w \leqslant 6\) | 15 |
| \(6 \lt w \leqslant 9\) | 12 |
| \(9 \lt w \leqslant 14\) | 9 |
(a) On the grid, draw a histogram for this information.
(3)
One of the parcels that Pedro delivered on Monday is chosen at random.
(b) Using the information in the table, find an estimate for the probability that this parcel weighs more than 7 kg. (2)
| Scheme | Marks |
|---|---|
| FD are: 6, 7, 5, 4, 1.8 | M1 |
| M1 | |
| A fully correct histogram gains full marks Answer: Correct histogram | A1 |
| (3) |
Notes
M1: For at least two frequency densities correct or at least two correct bars
M1: For at least 4 correct frequency densities or 4 correct bars
A1: Fully correct histogram
SCB2 for all five bars of correct width with heights in the correct ratio (eg drawn at 0.6, 0.7, 0.5, 0.4, 0.18)
SCB1 for three bars of correct width with heights in the correct ratio
| Scheme | Marks |
|---|---|
\(\left(9 + \dfrac{2}{3} \times 12\right)\) (= 17) oe eg 9 + 8 (= 17) or \(55 - \left(12 + 7 + 15 + \dfrac{1}{3} \times 12\right)\) | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{17}{55}\) | A1cao |
| (2) | |
| (5 marks) |
Notes
M1: may be seen as numerator of fraction
(ft their graph dep on M1 in (a))
A1cao: Or 0.30909… or 30.909….% (to at least 2 sf)
SCB1 for \(\dfrac{38}{55}\) (0.6909…)