State the conditions under which a Poisson distribution can be used as a suitable approximation for a Binomial distribution.
A network engineer claims that the probability of a data packet being corrupted during transmission over a specific fiber optic relay is 0.0008. A technician suspects that due to hardware degradation, the true probability of corruption is actually higher than 0.0008.
Define suitable null and alternative hypotheses to test the technician’s suspicion.
A random sample of 5000 data packets is monitored, and 9 are found to be corrupted.
Using a suitable approximation, test at the 5% level of significance whether there is sufficient evidence to support the technician's suspicion.
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.