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.
149 exam-style questions on OCR (MEI) A Level Maths 2.4.12 Calculate probabilities from a Normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.