2013 A-level H1 Mathematics (8864) Question 8 Suggested Solutions

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

(i)
Let X denote the number of batteries with lifetime of at least 100 hours, out of 10.

$X ~\sim~ \mathrm{B}(10, 0.8)$
$\mathrm{P} (X=10) = 0.107$

(ii)
$\mathrm{P} (X \ge 10) = 0.678$

(iii)
Let Y denote number of packs that satisfy the customer, out of 80.

$Y ~\sim~ \mathrm{B}(80, 0.6777995)$

Since $n = 80$ is large, $np = 54.224 > 5, nq = 25.776 >5$
$\Rightarrow Y ~\sim~ \mathrm{N}(54.224, 17.471)$ approximately

$\mathrm{P} (Y \ge 60)$
$= \mathrm{P} (Y \ge 59.5)$ by continuity correction

$\approx 0.103$

KS Comments

Remember to do 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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2013 A-level H1 Mathematics (8864) Question 8 Suggested Solutions

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