The time taken to fully charge the high-capacity battery of a specialized cargo drone follows a normal distribution with a mean of 140 minutes140\text{ minutes}140 minutes and a standard deviation of 12 minutes12\text{ minutes}12 minutes.
Determine the probability that a randomly selected battery charge takes longer than 155 minutes155\text{ minutes}155 minutes.
Any battery charge that takes longer than 155 minutes155\text{ minutes}155 minutes is classified as an "extended duration" charge.
A drone's battery charge is monitored at random. Given that it is classified as an extended duration charge,
calculate the probability that the charge takes longer than 165 minutes165\text{ minutes}165 minutes.
Among the extended duration charges, exactly 15%15\%15% last longer than m minutesm\text{ minutes}m minutes.
Find the value of mmm.
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.