A logistics company finds that 35% of their long-distance delivery drones require a battery recalibration after each flight.
State a distribution that is suitable to model the number of drones requiring recalibration in a random selection of 20 drones.
State two conditions for the distribution in part (a) to be a valid model.
Find the probability that: exactly 8 drones in a selection of 20 require recalibration,
Find the probability that: fewer than 12 drones in a selection of 40 require recalibration.
A maintenance supervisor notes that the technical team will be overwhelmed if more than 100 drones in a daily batch of 250 require recalibration.
Using a suitable approximation, find the probability that the technical team will be overwhelmed in a particular batch of 250 drones.
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.