Suppose the reaction temperature X in degree C in a certain

Suppose the reaction temperature X (in degree C) in a certain chemical process has a uniform distribution with A = -5 and 8 = 5. (a) Compute P(X

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 / (5-(-5)) = 1 / 10 = 0.1
Mean = a + b / 2 = 0
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 2.887
a)
P(X < 0) = (0-(-5)) * f(x)
= 5*0.1
= 0.5
b)
To find P(a < X < b) =( b - a ) * f(x)
P(-2.5 < X < 2.5) = (2.5--2.5) * f(x)
= 5*0.1
= 0.5

c)

To find P(a < X < b) =( b - a ) * f(x)
P(-2 < X < 4) = (4--2) * f(x)
= 6*0.1
= 0.6