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.
Practise Edexcel A Level Maths Finding Probabilities for Normal Distributions with exam-style questions for A Level Maths. 80 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
