A large-scale ecological study on urban honeybee colonies indicates that 40% of hives survive a particularly harsh winter without human intervention. A researcher monitors a random sample of 20 hives in a specific district.
Find the probability that exactly 7 of these hives survive.
Find the probability that at least 4 of these hives survive.
In a regional survey involving a larger sample of 150 hives, use a suitable approximation to determine the probability that the number of surviving hives is between 52 and 70 inclusive.
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.