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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.