Here is a question I can not seem to get from an error analysis course. Assume that you have a box of resistors that have a gaussian distribution of resisances with mean value mu=100 ohm and standard deviation sigma=20 ohm (20%resistors). Suppose that you wish to form a subgroup of resistors with mu= 100ohm and standard deviation of 5ohm (ie. 5%resistors) by selecting all resistors with resistance between the two limits r1= mu -a, and r2 = mu + a. a) find the value of a b) what fraction of the resistors should satisfy the condition? c) Find the standard deviation of the remaining sample. My problem is finding the value of a. At first glance I thought it would simply be 5, but after some thought it would appear that its more complicated than this because your taking from a sample. Also, I was not sure whether the new subgroup would follow a gaussian distribution. I'm having some troubles wrapping my head around this one. Can anyone help me get started?