| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2016 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Identify distribution and parameters |
| Difficulty | Easy -1.2 This is a straightforward S2 binomial distribution question requiring only basic recall and standard calculations. Part (a) tests understanding of sampling frames (simple conceptual point), part (b) requires identifying a binomial model B(20, 0.35) with minimal justification, and part (c) involves a routine calculator computation of P(X > 10). No problem-solving insight or multi-step reasoning is needed—this is easier than average A-level material. |
| Spec | 2.01d Select/critique sampling: in context2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Part (a) | Any suitable problem with using the database as a sampling frame: E.g. Might not be up to date, Might not contain all customers (incomplete), Might be biased | B1 |
| Part (b) | \(B(20, 0.35)\) | B1 dB1 |
| Part (c) | \(P(X > 10) = 1 - P(X \leq 10) = 1 - 0.9468 = 0.0532\) | M1 A1 |
| Total (5) |
| **Part (a)** | Any suitable problem with using the database as a sampling frame: E.g. Might not be up to date, Might not contain all customers (incomplete), Might be biased | B1 | Ignore extraneous non-contradictory comments. 'Not accurate' without context is not sufficient |
| **Part (b)** | $B(20, 0.35)$ | B1 dB1 | 1st B1 for $B$ or binomial which must be seen in part (b); 2nd B1 dependent on 1st B1 for $[n = 120, [p = ]0.35\text{oe}]$ which must be seen in part (b) |
| **Part (c)** | $P(X > 10) = 1 - P(X \leq 10) = 1 - 0.9468 = 0.0532$ | M1 A1 | M1 for writing or using $1 - P(X \leq 10)$; awrt **0.0532** |
| | | | Total (5) |
---The manager of a clothing shop wishes to investigate how satisfied customers are with the quality of service they receive. A database of the shop's customers is used as a sampling frame for this investigation.
\begin{enumerate}[label=(\alph*)]
\item Identify one potential problem with this sampling frame. [1]
\end{enumerate}
Customers are asked to complete a survey about the quality of service they receive. Past information shows that 35\% of customers complete the survey.
A random sample of 20 customers is taken.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down a suitable distribution to model the number of customers in this sample that complete the survey. [2]
\item Find the probability that more than half of the customers in the sample complete the survey. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2016 Q1 [5]}}