The amount of water in a 12ounce can has a uniform distribut

The amount of water in a 12-ounce can has a uniform distribution between 11.96 ounces and 12.05 ounces. What is the mean amount per can? What is the probability of selecting a can of water and finding it has less than 12 ounces? What is the probability of selecting a can of water and finding it has more than 11.98 ounces? What is the probability of selecting a can of water and finding it has more than 11.00 ounces?

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 / (12.05-11.96) = 1 / 0.09 = 11.1111
a)
Mean = a + b / 2 = 12.005
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 0.026
b)
P(X < 12) = (12-11.96) * f(x)
= 0.04*11.1111
= 0.444
c)
P(X > 11.98) = (12.05-11.98) * f(x)
= 0.07*11.1111
= 0.778
d)
P(X > 11) = (12.05-11) * f(x)
= 1.05*11.1111
= 11.667