| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Finding minimum stock level for demand |
| Difficulty | Standard +0.3 This is a straightforward Poisson distribution application requiring students to find P(X ≤ 4) and P(X > 2) with given parameters, then use inverse cumulative probability tables for part (c). While part (c) requires understanding of 'at most 5% chance' and table lookup, all parts follow standard S2 procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.02m Poisson: mean = variance = lambda |
| Answer | Marks | Guidance |
|---|---|---|
| (a) let X = no. of sales per week \(\therefore X \sim \text{Po}(8)\); \(P(X \le 4) = 0.0996\) | M1 A1 | |
| (b) let Y = no. of sales per day \(\therefore Y \sim \text{Po}(\frac{8}{5})\); \(P(Y > 2) = 1 - P(Y \le 2) = 1 - e^{-\frac{8}{5}}(1 + \frac{4}{5} + \frac{(\frac{8}{5})^2}{2}) = 1 - 0.8494 = 0.1506\) (4sf) | M1 M1 M1 A1 A1 | |
| (c) \(P(X \le 12) = 0.9362; P(X \le 13) = 0.9658\); \(\therefore\) need 13 in stock | M1 A1 A1 | (10 marks total) |
(a) let X = no. of sales per week $\therefore X \sim \text{Po}(8)$; $P(X \le 4) = 0.0996$ | M1 A1 |
(b) let Y = no. of sales per day $\therefore Y \sim \text{Po}(\frac{8}{5})$; $P(Y > 2) = 1 - P(Y \le 2) = 1 - e^{-\frac{8}{5}}(1 + \frac{4}{5} + \frac{(\frac{8}{5})^2}{2}) = 1 - 0.8494 = 0.1506$ (4sf) | M1 M1 M1 A1 A1 |
(c) $P(X \le 12) = 0.9362; P(X \le 13) = 0.9658$; $\therefore$ need 13 in stock | M1 A1 A1 | (10 marks total)
---4. A hardware store is open on six days each week. On average the store sells 8 of a particular make of electric drill each week.
Find the probability that the store sells
\begin{enumerate}[label=(\alph*)]
\item no more than 4 of the drills in a week,
\item more than 2 of the drills in one day.
The store receives one delivery of drills at the same time each week.
\item Find the number of drills that need to be in stock after a delivery for there to be at most a 5\% chance of the store not having sufficient drills to meet demand before the next delivery.\\
(3 marks)\\[0pt]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q4 [10]}}