2013 A-level H2 Mathematics (9740) Paper 2 Question 12 Suggested Solutions

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

(i)
The mean number of absences per day is constant.

(ii)

Let A be the number of absentees from Admin Department on n days.

$A~\sim~\mathrm{Po}(1.2n)$

$\mathrm{P}(A=0) = e^{-1.2n} < 0.01$

$n > 3.8$

$\therefore, \mathrm{smallest~number~of~days} = 4$

(iii)

Let T be the number of absentees from two Departments on 5 days.

$T~\sim~\mathrm{Po}(19.5)$

$\mathrm{P}(T>20) = 1- \mathrm{P}(T \le 20) = 0.397$

(iv)

Let S be the number of absentees from two Departments on 60 days.

$S~\sim~\mathrm{Po}(234)$

Since $\lambda = 234 > 10, S ~\sim~N(234, 234)$ approximately.

$\mathrm{P}(200 \le S \le 250) = \mathrm{P}(199.5 \le S \le 250.5) = 0.848$

KS Comments:

There are several answers to (i), please refer to school notes. Some students still forget to do continuity correction.

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KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. 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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2013 A-level H2 Mathematics (9740) Paper 2 Question 12 Suggested Solutions

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2013 A-level H2 Mathematics (9740) Paper 2 Question 12 Suggested Solutions

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