5 The examination marks obtained by 1200 candidates are illustrated on the cumulative frequency graph, where the data points are joined by a smooth curve.
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Use the curve to estimate
- the interquartile range of the marks,
- \(x\), if \(40 \%\) of the candidates scored more than \(x\) marks,
- the number of candidates who scored more than 68 marks.
Five of the candidates are selected at random, with replacement.
- Estimate the probability that all five scored more than 68 marks.
It is subsequently discovered that the candidates' marks in the range 35 to 55 were evenly distributed - that is, roughly equal numbers of candidates scored \(35,36,37 , \ldots , 55\).
- What does this information suggest about the estimate of the interquartile range found in part (i)?