Matching percentiles on two curves

Matching percentiles on two curves

Secondary 4
7 marks

The curves show the marks of the \(200\) candidates who sat Test 1 and the \(160\) candidates who sat Test 2.

  1. Amir scored \(60\) marks in Test 1. Find the percentage of Test 1 candidates who scored at most \(60\) marks.[1]
  2. Find the Test 2 mark that has the same percentage of Test 2 candidates at or below it.[2]
  3. Find the percentage of candidates in each test who scored more than \(80\) marks.[2]
  4. Ben says, “\(20\) candidates scored more than \(80\) marks in Test 2 and \(10\) in Test 1, so a Test 2 candidate was twice as likely to score more than \(80\).” Explain whether his conclusion is justified.[2]

Solution:

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Answer:(a) \(75\%\) (b) \(70\) marks (c) Test 1 \(5\%\), Test 2 \(12.5\%\) (d) Not justified: the totals differ; \(12.5\%\div5\%=2.5\), so a Test 2 candidate was \(2.5\) times as likely, not twice as likely, to score more than \(80\).

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