Suppose that the measured voltage in a certain electric circ

Suppose that the measured voltage in a certain electric circuit has a normal distribution with mean 120 and standard deviation 2. If three independent measurements of the voltage are made, what is the probability that all three measurements will lie between 116 and 118?

Solution

mu =120 and sigma = 2

Sample size =3

Prob (116<x<118)

Convert 116 and 118 to z score-2<z<-1

Prob for any one measurement to lie between these = P(-2<z<-1) =0.4772-0.3413

=0.1359

As all 3 areindependent prob forallthree measurement lying between these two

= 0.1359^3

=0.00251