An entomologist studies a population of beetles where the probability of an individual possessing iridescent wing cases is 0.2. A random sample of 20 beetles is collected.
Find the probability that in this sample there will be:
(i) exactly 3 beetles with iridescent wing cases,
(ii) at least 6 beetles with iridescent wing cases.
In a larger study, a sample of 250 beetles is collected. Use a suitable approximation to find the probability that the number of beetles with iridescent wing cases in this sample is more than 60.
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.