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.
