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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?

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?

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