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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.