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.
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.