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.
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.