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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.