Write down the median value.

A boy is chosen at random. Find the probability that he is shorter than $161{\text{ cm}}$.

Given that $82\%$ of the boys are taller than $h{\text{ cm}}$, find h .

${\text{median}} = 174 {\text{(cm)}}$     A1     N1

[1 mark]

attempt to find number shorter than 161     (M1)

e.g. line on graph, 12 boys

$p = \frac{{12}}{{200}}( = 0.06)$     A1     N2

[2 marks]

METHOD 1

$18\%$ have a height less than h     (A1)

$0.18 \times 200 = 36$ (36 may be seen as a line on the graph)     (A1)

$h = 166$ (cm)     A1     N2

METHOD 2

$0.82 \times 200 = 164$ (164 may be seen as a line on the graph)     (A1)

$200 - 164 = 36$     (A1)

$h = 166$ (cm)     A1     N2

[3 marks]

Parts (a) and (b) were generally well done.

Parts (a) and (b) were generally well done.

Some candidates could only earn the first mark in part (c) for finding $82\%$ of 200. Others gave the answer as 164, neglecting to subtract this value from the total of 200.