A maintenance engineer recorded the cavitation damage index, DDD, for 8 industrial water pumps. To simplify calculations, he used the coding v=D−kmv = \frac{D - k}{m}v=mD−k, where kkk and mmm are positive constants. His results are summarized in the table below.
| DDD | 105 | 125 | 95 | 115 | 90 | 130 | 100 | 120 |
|---|---|---|---|---|---|---|---|---|
| vvv | 5.0 | 9.0 | 3.0 | 7.0 | 2.0 | 10.0 | 4.0 | 8.0 |
Find the value of kkk and the value of mmm.
The engineer also recorded the total operating time, hhh thousand hours, for each of these 8 pumps. The data is summarised as follows:
Shh=6.40Svv=60.00Shv=17.50 S_{hh} = 6.40 \quad S_{vv} = 60.00 \quad S_{hv} = 17.50 Shh=6.40Svv=60.00Shv=17.50Calculate the product moment correlation coefficient (PMCC) between hhh and vvv.
State, with a reason, the value of the PMCC between hhh and DDD.
The engineer identifies the total accumulated damage and total load cycles for two further pumps, XXX and YYY.
| Pump | Total Accumulated Damage | Total Load Cycles |
|---|---|---|
| XXX | 63000 | 500 |
| YYY | 40000 | 400 |
Assuming the damage index DDD represents damage per load cycle, suggest which pump is most likely to have the higher operating time. Justify your answer.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.