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.
147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.