The continuous random variable WWW represents the mass of chemical residue, in milligrams, found in a 200 ml soil sample from a specific site. The distribution of WWW is a continuous uniform distribution over the interval [0,2.5][0, 2.5][0,2.5].
Determine P(W>2.0)P(W > 2.0)P(W>2.0).
State the value of E(W)E(W)E(W).
Calculate Var(W)Var(W)Var(W).
A random sample of 30 soil samples from this site is analysed.
Find the probability that fewer than 4 samples have a residue level of more than 2.0 mg.
When samples are taken from a different site, the residue level, XXX mg, is modelled by the cumulative distribution function F(x)F(x)F(x) where
F(x)={0x<00.1(x2+1.5x)0≤x≤2.51otherwise F(x) = \begin{cases} 0 & x < 0 \\ 0.1(x^2 + 1.5x) & 0 \le x \le 2.5 \\ 1 & \text{otherwise} \end{cases} F(x)=⎩⎨⎧00.1(x2+1.5x)1x<00≤x≤2.5otherwiseUsing this model, show that P(X>2.0)=0.3P(X > 2.0) = 0.3P(X>2.0)=0.3.
A random sample of 180 soil samples from this different site is taken.
Using a suitable approximation, find the probability that at least 60 of these samples have a residue level of more than 2.0 mg.
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.