Two satellite communication systems, Alpha and Beta, are being tested for signal latency. The latency of system Alpha, measured in milliseconds, is normally distributed with mean 85 and variance 12. The latency of system Beta, measured in milliseconds, is normally distributed with mean 81.5 and variance 18. The latencies for Alpha and Beta are independent. A single test packet is sent through each system.
Find the probability that the latency for the test packet on system Alpha is less than the latency on system Beta.
A transmission sequence consists of 60 packets. Assuming that the packets are sent simultaneously and all latencies are independent, find the probability that the total latency of system Alpha exceeds the total latency of system Beta by more than 250 milliseconds.
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.