2014 A-level H1 Mathematics (8864) Question 9 Suggested Solutions

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

(i)
(a)
Let X be the number of cakes containing fruit, out of 6.

$X ~\sim~ \mathrm{B} (6, 0.4)$

$\mathrm{P} (X = 0) = 0.0467$

(b)
$\mathrm{P} (X \le 2) = 0.544$

(ii)
Let Y be the number of packets with at most 2 cakes containing fruit, out of 8.

$Y ~\sim~ \mathrm{B} (8, 0.54432)$

$\mathrm{P} (Y \ge 4) = 1 - \mathrm{P}(Y \le 3) = 0.729$

(iii)
Let W be the number of packets with at most 2 cakes containing fruit, out of 150.

$W ~\sim~ \mathrm{B}(150, 0.54432)$

Since $n = 150$ is large, $np = 81.648 > 5$ and $nq = 68.352 > 5$ ,

$W ~\sim~ \mathrm{N}(81.648, 37.20536)$ approximately.

$\mathrm{P}(W > 75) = \mathrm{P}(W > 75.5)$ by continuity correction
$= 0.843$

KS Comments

Students must call all variables out carefully as they denote different things. And many still forget to perform continuity correction.

About

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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August 11th, 2015 11:09 PM

2014 A-level H1 Mathematics (8864) Question 9 Suggested Solutions

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