The reaction time X in minutes of a certain chemical process

The reaction time X (in minutes) of a certain chemical process follows a uniform distribution probability with 5 x 10. Draw the graph of the density curve. What is the probability that the reaction time is between six and eight minutes? What is the probability that the reaction time is between 5 and 8 minutes. What is the probability that the reaction time is less 6 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 / (10-5) = 1 / 5 = 0.2

Mean = a + b / 2 = 7.5
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 1.443
b)
To find P(a < X < b) =( b - a ) * f(x)
P(6 < X < 8) = (8-6) * f(x)
= 2*0.2
= 0.4

c)
P(5 < X < 8) = (8-5) * f(x)
= 3*0.2
= 0.6

d)
P(X < 6) = (6-5) * f(x)
= 1*0.2
= 0.2