The operating lifespan, LLL cycles, of Titan-X high-performance drone batteries is normally distributed with a mean of 450450450 cycles and a standard deviation of 404040 cycles.
Find the probability that a randomly selected Titan-X battery lasts for more than 530530530 cycles.
Batteries that exceed a lifespan of 530530530 cycles are designated as "Elite".
A battery is selected at random. Given that it is designated as Elite,
determine the probability that its lifespan exceeds 550550550 cycles.
Within the Elite category, exactly 15%15\%15% of batteries have a lifespan exceeding kkk cycles.
Find the value of kkk.
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.