An environmental study measured the concentration of a trace mineral, C C\,C mg/kg, in 80 soil samples taken from a specific region. The results were summarized as follows:
∑c=360and∑c2=2081 \sum c = 360 \quad \text{and} \quad \sum c^2 = 2081 ∑c=360and∑c2=2081(i) Calculate the mean concentration, cˉ\bar{c}cˉ. (ii) Calculate the standard deviation of CCC.
Assuming that the concentration C C\,C can be modelled by a normal distribution, find: (i) P(3<C<6)P(3 < C < 6)P(3<C<6) (ii) P(C=5.0)P(C = 5.0)P(C=5.0)
Determine, with a reason, whether a normal distribution is a suitable model for the mineral concentration in this region.
In a different region, the concentration D D\,D mg/kg is known to follow a normal distribution with a standard deviation of 1.2. Given that P(D<2.5)=0.01P(D < 2.5) = 0.01P(D<2.5)=0.01, find the value of the mean concentration μ \mu\,μ for this region, correct to three significant figures.
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.