2022 YIJC P2 Q9
2022 YIJC P2 Q9
8 marks
Prelims
A flower shop makes \(75\) bouquets of flowers daily. On average, \(p\%\) of the bouquets have LED lights. Assume that \(X\), the number of bouquets of flowers with LED lights made daily, follows a binomial distribution.
- Given that there is a probability of \(0.0288\) that fewer than \(2\) bouquets made in a day have LED lights, write down an equation in terms of \(p\) and hence find \(p\) correct to \(4\) decimal places.[3]
It is now given that \(p=7.5\).
- Find the most likely number of bouquets with LED lights made in a day.[2]
- \(30\) days are randomly selected. Find the probability that the mean number of bouquets with LED lights made per day is least \(5\).[3]
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Answer:(a) \({6.9977}\) (\(4\) d.p.) (b) The most likely number of bouquets with LED lights made in a day is \({5}\). (c) \({0.933}\) (\(3\) d.p.)
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