2022 JPJC P2 Q8
2022 JPJC P2 Q8
12 marks
Prelims
On average, \(72\) out of \(100\) students in a school complete online Mathematics homework by the deadline. The number of students in a class of \(n\) students who complete online Mathematics homework by the deadline is denoted by \(M\). State, in context, two assumptions needed for \(M\) to be well-modelled by a binomial distribution.[2]
Assume now that \(M\) has a binomial distribution.
- By taking \(n=25\),
- find the probability that fewer than \(15\) students in a class complete the online Mathematics homework by the deadline.[2]
- \(10\) classes with \(n\) students each are chosen at random from the school. Find the probability that exactly \(3\) of these classes have fewer than \(15\) students who complete the online Mathematics homework by the deadline.[2]
- \(30\) classes with \(n\) students each are chosen at random from the school. Find the probability that the mean number of students who complete the online Mathematics homework by the deadline per class is more than \(19\).[3]
- Find the least value of \(n\) such that there is greater than \(70\%\) chance that at least \(20\) students in a class complete the online Mathematics homework by the deadline.[3]
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Answer:(a)(i) \(\mathrm{P}\left( M<15 \right)\approx \mathrm{0}\mathrm{.0636}\) (ii) Required probability\(\approx \mathrm{0}\mathrm{.0195}\) (iii) \(\mathrm{P}\left( \overline{M}>19 \right)\approx 0.00735\) (b) \(n\ge 29\)
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