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.
