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 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.