| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Normal approximation to binomial |
| Difficulty | Standard +0.3 This is a straightforward application of binomial distribution with clearly stated parameters (n=10, p=0.35) and a normal approximation for larger n=80. Part (a) requires direct binomial probability calculations, while part (b) involves a routine normal approximation with continuity correction. The question is slightly easier than average because it's a standard textbook exercise with no conceptual challenges—students simply need to identify the distribution and apply formulas correctly. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.04d Normal approximation to binomial |
| Answer | Marks |
|---|---|
| let \(X\) = no. out of 10 shares that have gone up \(\therefore X \sim B(10, 0.35)\) | M1 |
| (i) \(P(X = 6) = 0.9740 - 0.9051 = 0.0689\) | M1 A1 |
| (ii) \(P(> 5 \text{ gone down}) = P(X \le 4) = 0.7515\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| let \(Y\) = no. out of 80 shares that have gone down \(\therefore Y \sim B(80, 0.65)\) | M1 | |
| \(N \text{ approx. } D \sim N(52, 18.2)\) | M1 A1 | |
| \(P(Y > 55) = P(D > 55.5)\) | M1 | |
| \(= P\left(Z > \frac{55.5 - 52}{\sqrt{18.2}}\right) = P(Z > 0.82)\) | A1 | |
| \(= 1 - 0.7939 = 0.2061\) | A1 | (11) |
**Part (a)**
let $X$ = no. out of 10 shares that have gone up $\therefore X \sim B(10, 0.35)$ | M1 |
(i) $P(X = 6) = 0.9740 - 0.9051 = 0.0689$ | M1 A1 |
(ii) $P(> 5 \text{ gone down}) = P(X \le 4) = 0.7515$ | M1 A1 |
**Part (b)**
let $Y$ = no. out of 80 shares that have gone down $\therefore Y \sim B(80, 0.65)$ | M1 |
$N \text{ approx. } D \sim N(52, 18.2)$ | M1 A1 |
$P(Y > 55) = P(D > 55.5)$ | M1 |
$= P\left(Z > \frac{55.5 - 52}{\sqrt{18.2}}\right) = P(Z > 0.82)$ | A1 |
$= 1 - 0.7939 = 0.2061$ | A1 | (11)
---As part of a business studies project, 8 groups of students are each randomly allocated 10 different shares from a listing of over 300 share prices in a newspaper. Each group has to follow the changes in the price of their shares over a 3-month period.
At the end of the 3 months, 35\% of all the shares in the listing have increased in price and the rest have decreased.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that, for the 10 shares of one group,
\begin{enumerate}[label=(\roman*)]
\item exactly 6 have gone up in price,
\item more than 5 have gone down in price. [5 marks]
\end{enumerate}
\item Using a suitable approximation, find the probability that of the 80 shares allocated in total to the groups, more than 35 will have decreased in value. [6 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q5 [11]}}