Higher January 2021 Paper 2 Q15
15 A postman records the weight of each parcel that he delivers.
The histogram shows information about the weights of all the parcels that the postman delivered last Monday. No parcels weighed more than 6 kg.
63 of the parcels that the postman delivered last Monday each had a weight between 0.5 kg and 2 kg.
The postman picks at random two of the records of the parcels he delivered last Monday.
| Scheme | Marks |
|---|---|
| 63 ÷ 1.5 (= 42) or a correct value written on FD scale (10 small squares = FD 10) or 10 squares = 1 parcel or 1 big square = 2.5 parcels oe eg area = 18 × 5 + 15 × 42 + 10 × 24 + 10 × 30 + 20 × 8 (= 1420) 3.6 × 1 + 3 × 8.4 + 2 × 4.8 + 2 × 6 + 4 × 1.6 (= 56.8) (at least 3 bars correct for any method of summing area) | M1 |
| 0.5 × 18 + 63 + 1 × 24 + 1 × 30 + 2 × 8 (9 + 63 + 24 + 30 + 16) oe eg “1420” ÷ 10 or “56.8” × 2.5 oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 142 | A1 |
| (3) |
Notes
M1: For use of area related to frequency eg showing a correct unambiguous value on the frequency density scale or calculating the area in some form
M1: Total of 5 frequencies with just one error or
Area of bars with just one error, with correct calculation to give frequency
| Scheme | Marks |
|---|---|
| 0.75 × 24 (= 18) + 30 + 16 (= 64) oe Eg “their (a)” – (9 + 63 + 0.25 × 24) (= 64) (ft figures from (a) dep on M1 for (a)) | M1ft |
| \(\dfrac{\text{“}64\text{”}}{142} \times \dfrac{\text{“}63\text{”}}{141}\) (ft their value of 142 from (a)) | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{672}{3337}\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1ft: (dep on M1 in (a)) if working with small squares they may get eg \(\dfrac{640}{1420}\)
M1: 64 must come from correct working allow \(\dfrac{\text{“}64\text{”}}{142} \times \dfrac{\text{“}64\text{”}}{142}\) (ft their value of 142 from (a))
A1: 0.201 or better (0.20137…)