A new battery supposedly with a charge of 15 volts actually

A new battery supposedly with a charge of 1.5 volts actually has a voltage with a uniform distribution between 1.43 and 1.60 volts.

. What is the standard deviation of the voltage?

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 / (1.6-1.43) = 1 / 0.17 = 5.8824
P(X < 10) = (10-1.43) * f(x)
= 8.57*5.8824
= 50.412

Mean = a + b / 2 = 1.515
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 0.049