The rate of oxygen consumption for a specific species of deep-sea bacteria, measured in μmol/h\mu \text{mol/h}μmol/h, is normally distributed with mean 15.415.415.4 and standard deviation 2.82.82.8. A marine biologist collects a random sample of nnn such bacteria. Determine the minimum sample size nnn such that the probability of the sample mean oxygen consumption exceeding 16.5 μmol/h16.5 \, \mu \text{mol/h}16.5μmol/h is less than 1%1\%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.