A laboratory centrifuge operates at discrete vibration stages V V\,V where V∈{1,2,3,4,5,6,7,8}V \in \{1, 2, 3, 4, 5, 6, 7, 8\}V∈{1,2,3,4,5,6,7,8}, and each stage is equally likely to occur during a test cycle.
Determine the mean and the variance of VVV.
The centrifuge is monitored over 60 independent test cycles. By applying the Central Limit Theorem, calculate an estimate for the probability that the average vibration stage Vˉ\bar{V}Vˉ of these 60 cycles is less than 4.1.
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.