An engineer is testing the efficiency of a high-performance lithium-polymer battery pack for an industrial drone. During a controlled test flight, the engineer records the flight duration, TTT minutes, and the terminal voltage, VVV volts, of the battery pack. A random sample of 8 readings was taken during the first 40 minutes of flight, as shown in the table below:
| TTT (min) | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
|---|---|---|---|---|---|---|---|---|
| VVV (volts) | 12.35 | 12.12 | 11.85 | 11.60 | 11.38 | 11.10 | 10.88 | 10.60 |
You may use the following summary statistics:
∑T=180 \sum T = 180 ∑T=180 ∑V=91.88 \sum V = 91.88 ∑V=91.88 STT=1050 S_{TT} = 1050 STT=1050 SVV=2.6064 S_{VV} = 2.6064 SVV=2.6064 ∑TV=2015.0 \sum TV = 2015.0 ∑TV=2015.0Calculate the value of STVS_{TV}STV.
Find the equation of the regression line of VVV on TTT in the form V=a+bTV = a + bTV=a+bT. Give the values of aaa and bbb correct to 3 significant figures.
Use your equation to estimate the terminal voltage of the battery pack after 18 minutes of flight.
Comment on the reliability of your estimate in (c), giving a mathematical reason for your answer.
A specialized long-range mission requires the drone to fly for 90 minutes.
Give a reason why the equation in (b) should not be used to estimate the battery voltage for this mission.
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.