A continuous random variable is uniformly distributed betwee

\"A continuous random variable is uniformly distributed between 100 and 150. a. What is the probability a randomly selected value
will be greater than 135? b. What is the probability a randomly selected value
will be less than 115? c. What is the probability a randomly selected value
will be between 115 and 135?\"
Please explain what was done to get the answer in understandable terms. Thanks.

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 = 125
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 14.434

f(x) = 1/(b-a) = 1 / (150-100) = 1 / 50 = 0.02
a)
P(X > 135) = (150-135) * f(x)
= 15*0.02
= 0.3

b)
P(X < 115) = (115-100) * f(x)
= 15*0.02
= 0.3

c)
To find P(a < X < b) =( b - a ) * f(x)
P(115 < X < 135) = (135-115) * f(x)
= 20*0.02
= 0.4