| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Identify distribution and parameters |
| Difficulty | Moderate -0.3 This is a straightforward S2 binomial distribution question with standard parts: identifying the distribution (trivial), calculating P(X≥4) using tables/calculator, finding minimum n for a probability condition (routine inequality), and applying normal approximation. All parts follow textbook templates with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Distribution \(X \sim B(n, 0.1)\) | B1 | For "binomial" or \(B(\ldots\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(Y \sim B(10, 0.1)\) | B1 | Writing or using \(B(10, 0.1)\) |
| \(P(Y \geq 4) = 1 - P(Y \leq 3) = 1 - 0.9872\) | M1 | Writing or using \(1 - P(Y \leq 3)\) |
| \(= 0.0128\) | A1 | awrt 0.0128 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(0.9^n < 0.05\) or \(1 - (0.9)^n > 0.95\) | M1 | oe, or \((0.9)^n = 0.05\), oe, or seeing 0.0523 or 0.0471 |
| \(n > 28.4\) | A1 | \([P(0)] = 0.0471\) or awrt 28.4 |
| \(n = 29\) | A1 | cao; \(n = 29\) should not come from incorrect working |
| *Alternative:* \(B(28,0.1): P(0) = 0.0523\); \(B(29,0.1): P(0) = 0.0471\); \(n = 29\) | M1, A1, A1cao | NB answer of 29 on its own with no working gains M1A1A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(C \sim Po(5)\) | B1 | Writing or using \(Po(5)\) |
| \(P(C > 10) = 1 - P(C \leq 10) = 1 - 0.9863\) | M1 | Writing or using \(1 - P(C \leq 10)\) |
| \(= 0.0137\) | A1 | awrt 0.0137 |
# Question 7:
## Part 7(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Distribution $X \sim B(n, 0.1)$ | B1 | For "binomial" or $B(\ldots$ |
## Part 7(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $Y \sim B(10, 0.1)$ | B1 | Writing or using $B(10, 0.1)$ |
| $P(Y \geq 4) = 1 - P(Y \leq 3) = 1 - 0.9872$ | M1 | Writing or using $1 - P(Y \leq 3)$ |
| $= 0.0128$ | A1 | awrt 0.0128 |
## Part 7(c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $0.9^n < 0.05$ or $1 - (0.9)^n > 0.95$ | M1 | oe, or $(0.9)^n = 0.05$, oe, or seeing 0.0523 or 0.0471 |
| $n > 28.4$ | A1 | $[P(0)] = 0.0471$ or awrt 28.4 |
| $n = 29$ | A1 | cao; $n = 29$ should not come from incorrect working |
| *Alternative:* $B(28,0.1): P(0) = 0.0523$; $B(29,0.1): P(0) = 0.0471$; $n = 29$ | M1, A1, A1cao | NB answer of 29 on its own with no working gains M1A1A1 |
## Part 7(d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $C \sim Po(5)$ | B1 | Writing or using $Po(5)$ |
| $P(C > 10) = 1 - P(C \leq 10) = 1 - 0.9863$ | M1 | Writing or using $1 - P(C \leq 10)$ |
| $= 0.0137$ | A1 | awrt 0.0137 |
The image provided appears to be only the back/credits page of an Edexcel publication (Summer 2013, Order Code UA036999), which contains only publisher information, contact details, and logos for Ofqual, Welsh Assembly Government, and CEA.
There is **no mark scheme content** visible on this page — no questions, answers, mark allocations, or guidance notes are present to extract.
If you have additional pages from this mark scheme, please share them and I'll be happy to extract and format the content as requested.\begin{enumerate}
\item A telesales operator is selling a magazine. Each day he chooses a number of people to telephone. The probability that each person he telephones buys the magazine is 0.1\\
(a) Suggest a suitable distribution to model the number of people who buy the magazine from the telesales operator each day.\\
(b) On Monday, the telesales operator telephones 10 people. Find the probability that he sells at least 4 magazines.\\
(c) Calculate the least number of people he needs to telephone on Tuesday, so that the probability of selling at least 1 magazine, on that day, is greater than 0.95
\end{enumerate}
A call centre also sells the magazine. The probability that a telephone call made by the call centre sells a magazine is 0.05 The call centre telephones 100 people every hour.\\
(d) Using a suitable approximation, find the probability that more than 10 people telephoned by the call centre buy a magazine in a randomly chosen hour.
\hfill \mbox{\textit{Edexcel S2 2013 Q7 [10]}}