A geochemist is determining the concentration of a rare isotope in a lunar soil sample. The concentration of the isotope in the sample is c c\,c parts per million (ppm). The measured concentration, C C\,C ppm, is modeled by a normal distribution with mean c c\,c and standard deviation 1.4 ppm.
Determine the probability that a single measurement C C\,C lies within 2.1 ppm of the true concentration ccc.
The geochemist takes a random sample of 49 independent measurements of the isotope concentration from the same soil sample.
Calculate the probability that the sample mean of these 49 measurements, Cˉ\bar{C}Cˉ, is within 0.45 ppm of ccc.
The mean of this sample of 49 measurements is found to be 425.6 ppm. Construct a 95% confidence interval for ccc, giving your limits to three decimal places.
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.