The volume of excess reagent, VVV (in litres), produced in a chemical reaction is modelled by the probability density function
f(v)={kv(25−v2)0≤v≤50otherwise f(v) = \begin{cases} kv(25 - v^2) & 0 \le v \le 5 \\ 0 & \text{otherwise} \end{cases} f(v)={kv(25−v2)00≤v≤5otherwiseShow that k=4625k = \frac{4}{625}k=6254.
Using integration, determine:
the mean volume of excess reagent produced per reaction,
the probability that a reaction produces more than 3 litres of excess reagent.
Three independent reactions are carried out.
Find the probability that at least 2 of these reactions produce more than 3 litres of excess reagent.
