the distribution of days to find a doctor with an Obamacare

the distribution of days to find a doctor with an Obamacare policy is uniform with a minimum of 10 and maximum value of 35 days. What is the probability of finding a doctor in less than 20 days?

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 )
Mean = a + b / 2 = 22.5
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 7.217

f(x) = 1/(b-a) = 1 / (35-10) = 1 / 25 = 0.04
P(X < 20) = (20-10) * f(x)
= 10*0.04
= 0.4