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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.