The duration, T T\,T in hours, of a specific industrial chemical reaction is modeled by the probability density function
f(t)={kt(16−t2)0≤t≤40otherwise f(t) = \begin{cases} kt(16 - t^2) & 0 \le t \le 4 \\ 0 & \text{otherwise} \end{cases} f(t)={kt(16−t2)00≤t≤4otherwiseShow that k=164\displaystyle k = \frac{1}{64}k=641.
Using integration, find
the mean duration of the reaction,
the probability that a reaction lasts for more than 3 hours.
Three independent reactions are monitored.
Determine the probability that at least 2 of the reactions last for more than 3 hours.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
