14. Correct. The answer is false. 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 = 5/8
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