State the conditions under which the Normal distribution can be used as an approximation to the Binomial distribution.
A marine biologist claims that the proportion of leatherback turtle hatchlings that successfully reach the ocean from their nests is 0.42. A local conservationist believes that a new beach-lighting initiative has improved this survival rate.
State suitable null and alternative hypotheses to test the conservationist's belief.
To investigate this claim, a random sample of 150 hatchlings is observed, and it is found that 75 of them successfully reached the ocean.
Using a suitable approximation, test at the 5% level of significance whether or not there is evidence to support the conservationist's belief.
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.