Foundation June 2022 Paper 2 Q17
17 Morgan is playing a computer game.
They can score 0, 1, 2 or 3 points on each turn.
They record their scores for 100 turns.
The table shows the relative frequencies of their scores.
| Score | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Relative frequency | 0.08 | 0.42 | 0.38 |
(a) Complete the table. [2]
(b) Morgan says
I scored more than 160 points in total in my 100 turns.
Is Morgan correct?
Show how you decide. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [0].12 oe | 2 | M1 for \(1 - (0.08 + 0.42 + 0.38)\) oe | Accept e.g. 12%, 12/100 oe M1 implied by \(1 - 0.88\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 154 [points] and | 4FT | B3 for 154 or \(118 + 3 \times \textit{their}\ 0.12 \times 100\) correctly evaluated or M2 for \([0.08 \times 0 \times 100 +]\ ([1 \times]\ 0.42 \times 100) + (2 \times 0.38 \times 100) + (3 \times \textit{their}\ 0.12 \times 100)\) or better or M1 for \(2 \times 0.38\) and \(3 \times \textit{their}\ 0.12\) or for one of \(([1 \times]\,0.42 \times 100)\), \((2 \times 0.38 \times 100)\), \((3 \times \textit{their}\ 0.12 \times 100)\) | M2 for full method implied by \(42 + 76 + 36\) or \(1.54 \times 100\) M1 implied by [0].76 and [0].36 or 1.54 or one of 42, 76, 36 |
| No/Morgan is not correct oe | FT dep on B3 for correct conclusion from their 0.12 | For conclusion accept e.g. 154 and No, \(154 \lt 160\) If FT from e.g. 0.22 in (a) then 184 and yes gets 4FT | |