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 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.