Foundation June 2024 Paper 2 Q25
25 A machine makes bolts that should be 30.0 mm long, correct to 1 decimal place.
Jane checks the accuracy of the machine by taking a random sample of 10 of the bolts.
Here are the lengths, in mm correct to 1 decimal place, of the bolts in Jane’s sample.
\[29.5 \quad 29.1 \quad 30.0 \quad 30.0 \quad 30.2 \quad 30.0 \quad 30.0 \quad 30.0 \quad 30.5 \quad 30.0\]The machine makes 2000 of these bolts that day.
Jane says
6 of the 10 bolts in the sample are of the correct length. That is 60%.
Therefore, 1200 of the 2000 bolts will be of the correct length because that is 60%.
Give a reason why Jane’s claim may be unreliable. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Correct reason given e.g. Her sample may not be representative oe Her sample is too small oe | 1 | She should do the test more than 10 times She should do the test e.g. 100/1000 times. Mark best response as long as not contradictory or incorrect See Appendix 4 | |
Appendix
APPENDIX 4 Question 25
| Response | Mark | |
|---|---|---|
| 1 | The machine took a random sample so it will not always be 6 bolts out of 10 to the correct length (implies not representative) | 1 |
| 2 | Janes claim may be unreliable as she only did 1 sample and it might not be 60% all the time (‘only’ implies too small a sample) | 1 |
| 3 | Because she’s only checked 10 out of thousands so she needs to check a higher amount to measure probability | 1 |
| 4 | Because not every 10 bolts will have 6 correct ones | 1 |
| 5 | 6/10 of the bolts may not always be 6/10 it could be 4/10 she needs to do the test again | 1 |
| 6 | Only collects 10 bolts (implies small sample) | 1 |
| 7 | It’s a random selection | 0 |
| 8 | Because the more samples you have the more unreliable it is | 0 |
| 9 | Because she hasn’t sampled all 2000 bolts meaning she cannot claim 1200 are of the correct length | 0 |
| 10 | They may not be reliable because her evidence on these lengths are facts its not 60% | 0 |
| 11 | Because they have to be correct to 1 decimal place | 0 |
| 12 | The machine took a random sample so it will not always be 6 bolts to the correct length (not enough) | 0 |
| 13 | Only an estimate | 0 |
| 14 | Because there could be more or less bolts which are longer or shorter | 0 |
| 15 | Might not be accurate, and she is going off the 10 bolts (Not as good as Exemplar 6, ‘only’ needs a reference here) | 0 |