14. Incorrect. The answer is false, not true. Since a supervisor can arrive to the control point at whatever moment and all the moments are equally possible, the random variable X follows a uniform distribution in an interval [a,b] of length b - a = 8. Considering a = 0 and b = 8, the density function of X is:

The cumulative distribution function is:

a) Let A be the event: 'a supervisor waits less than 5 minutes'. A means that 'X' can take values between 0 a 5 minutes. Therefore:

P[A] = P[X < 5] = F[5] = 5/8

b) Let B the event: 'a supervisor waits more than 2 minutes'.

P[B] = P[X > 2] = 1 - P[X ≤ 2] = 1 - 2/8 = 3/4