2010 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

September 23, 2015

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Let $X =$ number of calls in a period of 4minutes.

$X \sim \text{Po}(4 \times 3) = \text{Po}(12)$

$\text{P}(X=8) = 0.0655$

(ii)
Let $t =$ length of time

Let $Y =$ number of calls in a period of $t$ minutes.

$Y \sim \text{Po}(3t)$

$\text{P}(Y=0) = 0.2$

$e^{-3t} = 0.2$

$t = 0.53648$ minutes
$t = 32$ seconds

(iii)
Let $W =$ number of calls in a working day of 12 hours.

$W \sim \text{Po}(2160)$

Since $\lambda =2160 > 10, W \sim \text{N}(2160, 2160)$ approximately

$\text{P}(W>2200)$

$= \text{P}(W>2200.5)$ by continuity correction

$= 0.192$

(iv)
Let $V =$ number of busy days out of 6 working days.

$V \sim \text{B}(6, 0.19176)$

$\text{P} (V=2) = 0.235$

(v)
Let $U =$ number of busy days out of 30 working days.

$U \sim \text{B}(30, 0.19176)$

Since $n=30$ is large, $np-5.7528 > 5, n(1-p) = 24.2472 >5$

$U \sim \text{N}(5.7528, 4.6496)$ approximately

$\text{P}(U \textless 10)$

$\text{P}(U \textless 9.5)$ by continuity correction

$= 0.959$

9740 A-level A-levels H2 Mathematics Paper 2 Pure Mathematics Statistics Suggested Solutions Year 2010

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KS has been teaching H2/H1 Mathematics and IB mathematics for almost two decades. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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