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 (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.