The number of white house tours this year are uniformly dist

The number of white house tours this year are uniformly distributed with a min = 0 and max = 30. What is the probability that sending a text will be between 15 and 20 tours

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 / (30-0) = 1 / 30 = 0.0333
Mean = a + b / 2 = 15
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 8.66

To find P(a < X < b) =( b - a ) * f(x)
P(15 < X < 20) = (20-15) * f(x)
= 5*0.0333
= 0.167