| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Exact binomial then normal approximation (same context, different n) |
| Difficulty | Standard +0.3 This is a straightforward S2 question requiring basic binomial probability calculations in parts (a) and (b), then a standard normal approximation to binomial in part (c). The setup is clear, the probability is given (p=6/15=0.4 for red), and part (c) follows a textbook procedure (check np>5, apply continuity correction, standardize). Slightly above average difficulty only because it combines multiple techniques across three parts, but each step is routine for S2 students. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.04d Normal approximation to binomial |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(R \sim B(15, 0.4)\); \(P(R < 2) = P(R \leq 1) = 0.0052\) | B1 M1 A1 | |
| (b) \(P(R \geq 8) = 1 - P(R \leq 7) = 1 - 0.7869 = 0.213\) | M1 A1 | |
| (c) Number of greens is \(G \sim B(150, 0.6) \approx N(90, 36)\) | M1 A1 | |
| \(P(G > 100.5) = P(Z > 10.5/6) = P(Z > 1.75) = 0.0401\) | M1 A1 M1 A1 A1 | Total: 12 marks |
(a) $R \sim B(15, 0.4)$; $P(R < 2) = P(R \leq 1) = 0.0052$ | B1 M1 A1 |
(b) $P(R \geq 8) = 1 - P(R \leq 7) = 1 - 0.7869 = 0.213$ | M1 A1 |
(c) Number of greens is $G \sim B(150, 0.6) \approx N(90, 36)$ | M1 A1 |
$P(G > 100.5) = P(Z > 10.5/6) = P(Z > 1.75) = 0.0401$ | M1 A1 M1 A1 A1 | Total: 12 marks\begin{enumerate}
\item Lupin seeds are sold in packets of 15 . On average, 9 seeds in a packet are green and 6 are red. Find, to 2 decimal places, the probability that in any particular packet there are\\
(a) less than 2 red seeds,\\
(b) more red than green seeds.
\end{enumerate}
The seeds from 10 packets are then combined together.\\
(c) Use a suitable approximation to find the probability that the total number of green seeds is more than 100 .\\
\hfill \mbox{\textit{Edexcel S2 Q5 [12]}}