The waiting time in minutes, XXX, of a customer at a cafe is modelled by the probability density function
f(x)={kx(36−x2)0≤x≤60otherwise f(x) = \begin{cases} kx(36 - x^2) & 0 \le x \le 6 \\ 0 & \text{otherwise} \end{cases} f(x)={kx(36−x2)00≤x≤6otherwiseShow that k=1324k = \frac{1}{324}k=3241.
Using integration, find
the mean waiting time of a customer,
the probability that a customer will wait for more than 4 minutes.
Three independent customers visit the cafe.
Find the probability that at least 2 of the customers wait for more than 4 minutes.
