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.
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.