2025 ASRJC P2 Q10

Green Earth Factory produces solar panels. On average, \(2\)% of the solar panels produced are found to contain defects. The solar panels are packed in batches of \(10\).

1. State, in the context of solar panel production, two assumptions needed for the number of defective solar panels in a batch to be well modelled by a binomial distribution.[2]

It is now given that the number of defective solar panels per batch follows a binomial distribution.

2. Find the probability that a batch contains at least \(2\) defective solar panels.[2]

As part of Green Plan initiative, the Education Department plans to install solar panels on the rooftops of \(100\) primary schools to reduce carbon footprint. Each school will be fitted with \(10\) solar panels, and the school will lodge a complaint if there are at least two defective panels in their allocation.

3. Find the probability that at most \(5\) schools lodge complaints.[2]

Green Earth Factory also produces LED lights with a defect rate of \(1\)%. The number of defective LED lights also follows a binomial distribution. As part of the same green initiative, the Education Department orders installations for the \(100\) primary schools, with each school receiving another \(25\) LED lights. For quality control purposes, the Education Department will fine the factory if the total number of defective items (combining both solar panels and LED lights) across all \(100\) schools exceeds \(50\) units.

4. By using an approximation, find the probability that Green Earth Factory receives a fine.[5]