N2015 P2 Q10

N2015 P2 Q10

Junior College 2
9 marks

In an experiment the following information was gathered about air pressure \(P\), measured in inches of mercury, at different heights above sea-level \(h\), measured in feet.

\(h\)\(2000\)\(5000\)\(10000\)\(15000\)\(20000\)\(25000\)\(30000\)\(35000\)\(40000\)\(45000\)
\(P\)\(27.8\)\(24.9\)\(20.6\)\(16.9\)\(13.8\)\(11.1\)\(8.89\)\(7.04\)\(5.52\)\(4.28\)
  1. Draw a scatter diagram for these values, labelling the axes.[1]
  2. Find, correct to \(4\) decimal places, the product moment correlation coefficient between[3]
    1. \(h\) and \(P\),
    2. \(\ln h\) and \(P\),
    3. \(\sqrt h\) and \(P\).
  3. Using the most appropriate case from part (ii), find the equation which best models air pressure at different heights.[3]
  4. Given that \(1\) metre \(=3.28\) feet, re-write your equation from part (iii) so that it can be used to estimate the air pressure when the height is given in metres.[2]

Solution:

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Answer:(ii)(a) \(-0.9807\) (b) \(-0.9748\) (c) \(-0.9986\) (iii) \(P\approx34.8-0.147\sqrt h\) (iv) \(P\approx34.8-0.266\sqrt H\), \(H\) in metres.

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