| Date | May 2017 | Marks available | 2 | Reference code | 17M.2.sl.TZ1.4 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Hence and Find | Question number | 4 | Adapted from | N/A |
Question
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 \(k\).
Hence, find the probability that exactly \(k\) students are left handed;
Hence, find the probability that fewer than \(k\) students are left handed.
Markscheme
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]
