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.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.