Biologists monitoring a population of Arctic Terns have found that 15% of the birds possess a specific unique feather pigmentation. A random sample of 50 birds is captured and examined. Let X X\,X denote the number of birds in the sample with this pigmentation.
Suggest a suitable distribution to model XXX.
State one condition required for this model to be valid in this context.
The probability that fewer than k k\,k birds in the sample possess the pigmentation is less than 0.10.
Determine the largest possible integer value of kkk.
A second, much larger random sample of 200 birds is subsequently captured.
The probability that at least m m\,m of these birds possess the pigmentation is approximately 0.825.
Using a normal approximation, find the value of mmm.
Following a period of extreme climate change, a biologist takes a new random sample of 30 birds and finds that only 1 possesses the unique pigmentation.
Test, at the 5% level of significance, whether there is evidence that the proportion of birds with this pigmentation has decreased. State your hypotheses clearly.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.