Edexcel S2 2006 January — Question 4 4 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2006
SessionJanuary
Marks4
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Mark schemeDownload PDF ↗
TopicApproximating the Binomial to the Poisson distribution
TypeCalculate single probability using Poisson approximation
DifficultyStandard +0.3 This is a straightforward application of the Poisson approximation to the binomial distribution with n=150, p=0.02 giving λ=3. Students need to recognize when the approximation is valid (large n, small p), calculate the parameter, and find P(X>7) using tables or calculator. It's slightly above average difficulty due to being S2 content and requiring the inequality direction, but follows a standard procedure with no novel insight required.
Spec2.04b Binomial distribution: as model B(n,p)
4. The random variable \(X \sim \mathrm {~B} ( 150,0.02 )\). Use a suitable approximation to estimate \(\mathrm { P } ( X > 7 )\).
Question 4:
AnswerMarks Guidance
\(X = \text{Po}(150 \times 0.02) = \text{Po}(3)\)B1, B1(dep)
\(P(X>7) = 1 - P(X \leq 7)\)M1
\(= 0.0119\)A1 awrt 0.0119
*Note: Use of normal approximation max awards B0 B0 M1 A0 with \(z = \frac{7.5-3}{\sqrt{2.94}} = 2.62\), giving \(0.0047\)*
# Question 4:

| $X = \text{Po}(150 \times 0.02) = \text{Po}(3)$ | B1, B1(dep) | |
| $P(X>7) = 1 - P(X \leq 7)$ | M1 | |
| $= 0.0119$ | A1 | awrt 0.0119 |

*Note: Use of normal approximation max awards B0 B0 M1 A0 with $z = \frac{7.5-3}{\sqrt{2.94}} = 2.62$, giving $0.0047$*

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4. The random variable $X \sim \mathrm {~B} ( 150,0.02 )$.

Use a suitable approximation to estimate $\mathrm { P } ( X > 7 )$.\\

\hfill \mbox{\textit{Edexcel S2 2006 Q4 [4]}}
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Q1 7 Q2 8 Q3 8 Q4 4 Q5 15 Q6 13 Q7 19