Find $k$.

Hence, find the probability that exactly $k$ students are left handed;

Hence, find the probability that fewer than $k$ students are left handed.

evidence of binomial distribution (may be seen in part (b))     (M1)

eg$\,\,\,\,\,$$np,{\text{ }}150 \times 0.08$

$k = 12$     A1     N2

[2 marks]

${\text{P}}\left( {X = 12} \right) = \left( {\begin{array}{*{20}{c}} {150} \\ {12} \end{array}} \right){\left( {0.08} \right)^{12}}{\left( {0.92} \right)^{138}}$    (A1)

0.119231

probability $= 0.119$     A1     N2

[2 marks]

recognition that $X \leqslant 11$     (M1)

0.456800

${\text{P}}(X < 12) = 0.457$     A1     N2

[2 marks]