The continuous flight time, T T\,T minutes, of a specific industrial drone model is normally distributed with a mean of 45.0 minutes and a standard deviation of 4.0 minutes.
Using standardisation, show that the probability that a randomly selected battery for this drone lasts less than 41.0 minutes is 0.1587.
A logistics company requires a drone to complete a survey flight that demands a battery flight time of at least 41.0 minutes. To qualify for the task, the operator has up to 3 batteries available to test. Batteries are tested sequentially; as soon as a battery lasts more than 41.0 minutes, it qualifies and testing stops.
Given that a drone successfully qualifies for the task within the 3 available attempts, and assuming flight times for all batteries are independent,
determine the probability that the drone qualified on the second battery tested with a flight time exceeding 53.0 minutes.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.