For a non-homogeneous Poisson flow of customers, the intensity (t) during the first 8 hours is increasing

For a non-homogeneous Poisson flow of customers, the intensity λ(t) during the first 8 hours is increasing as 10(t/8)² [ending up with 10 customers/hour at the end of the period]. Find the expected value and the standard deviation of the number of customers during the whole period. Given that the fifth customer arrived at t = 5 h, find the probability that the sixth customer will arrive after 5h 6min.