| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2019 |
| Session | Specimen |
| Marks | 6 |
| Topic | Binomial Distribution |
| Type | Verify conditions in context |
| Difficulty | Moderate -0.3 This is a straightforward binomial distribution question requiring standard assumptions (independence, constant probability) and a routine calculation of P(X ≤ 2). The conceptual demand is low—recognizing when binomial applies and computing cumulative probabilities—making it slightly easier than average but not trivial due to the multi-part structure and need for careful interpretation of 'fewer than 13%'. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
A survey into left-handedness found that 13% of the population of the world are left-handed.
\begin{enumerate}[label=(\alph*)]
\item State the assumptions necessary for it to be appropriate to model the number of left-handed children in a class of 20 children using the binomial distribution B(20, 0.13). [2]
\item Assuming that this binomial model is appropriate, calculate the probability that fewer than 13% of the 20 children are left-handed. [4]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2019 Q4 [6]}}