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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.