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

By KS Teng

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!!!

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