If we assume that actual flight times are uniformly distributed between 5 hours and 5 hours, 16 minutes, then the total possible range of flight times is 16 minutes, or 0.2667 hours.
Let X be the actual flight time. Then we can write:
X ~ U(5, 5.2667)
We want to find the probability that the flight will be more than 8 minutes late, or in other words, the probability that the actual flight time exceeds 5 hours and 12 minutes, which is 0.2 hours more than the scheduled flight time of 5 hours and 4 minutes.
So we need to find:
P(X > 5.2)
Using the uniform distribution formula for probability density function, we can compute:
f(x) = 1 / (5.2667 - 5) = 1 / 0.2667 = 3.75
Then we have:
P(X > 5.2) = ∫[5.2, 5.2667] f(x) dx
= ∫[5.2, 5.2667] 3.75 dx
= 3.75 * (5.2667 - 5.2)
= 0.25
Therefore, the probability that the flight will be more than 8 minutes late is 0.25, or 25%.