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.
67 exam-style questions on OCR A Level Maths 2.4.4 Mean and variance of the binomial (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.