The waiting times between a subway departure schedule and th

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time less than .75 minutes. Find the probability that a randomly selected passenger has a waiting time more than 3 minutes.

Solution

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )

f(x) = 1/(b-a) = 1 / (7-0) = 1 / 7 = 0.1429

Mean = a + b / 2 = 3.5
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 2.021

a)
P(X < 1.25) = (1.25-0) * f(x)
= 1.25*0.1429
= 0.179
b)
P(X > 3) = (7-3) * f(x)
= 4*0.1429
= 0.572