State the conditions under which a normal distribution can be used as a suitable approximation for a binomial distribution B(n,p)B(n, p)B(n,p).
A wholesale seed distributor claims that 35% of the seeds in their 'Azure Meadow' mix will produce blue-petalled flowers.
Explain why the distributor should not test every seed in a batch to verify this specific claim.
To investigate the distributor's claim, a researcher selects a random sample of 400 seeds and grows them under controlled conditions.
State the null and alternative hypotheses for a two-tailed test of the distributor’s claim.
Of the 400 seeds sampled, 156 were found to produce blue-petalled flowers.
Use a normal approximation to test, at the 5% level of significance, whether there is evidence to suggest the distributor's claim is incorrect.
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.