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.
67 exam-style questions on OCR A Level Maths 2.4.4 Mean and variance of the binomial (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.