Resistances of certain resistors are uniformly distributed o

Resistances of certain resistors are uniformly distributed on the interval between 95ohm and 103ohm. a. Find the mean resistance. b. Find the standard deviation of the resistances. c. What is the probability that the resistance is greater than 100 ohm? d. Suppose the resistances of different resistors are independent. What is the probability that three out of six resistors have resistance greater than 100 ohm?

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 / (103-95) = 1 / 8 = 0.125

a)
Mean = a + b / 2 = 99

b)
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 2.309

c)
P(X > 100) = (103-100) * f(x)
= 3*0.125
= 0.375