Higher January 2020 Paper 1 Q4
4 The table shows information about the weights, in kilograms, of 40 babies.
| Weight (\(w\) kg) | Frequency |
|---|---|
| \(2 \lt w \leqslant 3\) | 12 |
| \(3 \lt w \leqslant 4\) | 16 |
| \(4 \lt w \leqslant 5\) | 9 |
| \(5 \lt w \leqslant 6\) | 2 |
| \(6 \lt w \leqslant 7\) | 1 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean weight of the 40 babies. (4)
One of the 40 babies is going to be chosen at random.
(c) Find the probability that this baby has a weight of more than 5 kg. (2)
| Scheme | Marks |
|---|---|
| \(3 \lt w \leqslant 4\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| (12 × 2.5) + (16 × 3.5) + (9 × 4.5) + (2 × 5.5) + (1 × 6.5) or 30 + 56 + 40.5 + 11 + 6.5 (= 144) | M2 |
| [(12 × 2.5) + (16 × 3.5) + (9 × 4.5) + (2 × 5.5) + (1 × 6.5)] ÷ 40 or ‘144’ ÷ 40 | M1 |
| 3.6 | A1 |
| (4) |
Notes
M2: for at least 4 correct products added (need not be evaluated) or
If not M2 then award
M1 for consistent use of value within interval (including end points) for at least 4 products which must be added
or
correct midpoints used for at least 4 products and not added
M1: (dep on at least M1)
Allow division by their Σf provided addition or total under column seen
A1: oe
| Scheme | Marks |
|---|---|
| \(\dfrac{2}{40} + \dfrac{1}{40}\) | M1 |
| \(\dfrac{3}{40}\) | A1 |
| (2) | |
| (7 marks) |
Notes
M1: for \(\dfrac{a}{40}\) where \(0 \lt a \lt 40\) or \(\dfrac{3}{b}\) where \(b \gt 3\) where \(a\) and \(b\) are integers
A1: 0.075 oe