17M.2.SL.TZ1.S_4

pestleMathematicsAISLPaper 217M· sl-4-7-discrete-random-variablessource ↗

In a large university the probability that a student is left handed is 0.08. A sample of 150 students is randomly selected from the university. Let $k$ be the expected number of left-handed students in this sample.

Find $k$ .

[2]

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

[2]

b.i.

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

[2]

b.ii.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

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]

b.i.

recognition that $X \leqslant 11$ (M1)

0.456800

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

[2 marks]

b.ii.

Examiners’ report

[N/A]

b.i.

[N/A]

b.ii.