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.