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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.