Find n of 2 independent samples

[koborch]

Hello,
i have a problem with the following exercise. Could someone give me a hint how i can solve it?

X¯1 and X¯2 are means of two independent samples each of size n from the same
normally distributed population with variance σ².
Find n, such that:
P (|X¯1 − X¯2| < σ/5) = 0.95

 

[Dason]

Which part is giving you the most trouble? Is it the absolute value? Keep in mind that if c is positive then:

| x | < c
is the same as
-c < x < c

 

[koborch]

Yeah, we had similar exercises but never with the means of two independent samples in the absolute value..

 

[Dason]

Another tip for getting started on problems like these: if you don't know where to start just plug some stuff in. In this case you want to solve for n but what happens if you specify n ahead of time? If n = 1 can you figure out what the probability on the left hand side is? You have everything you need to be able to calculate it. What about for n = 2? Once you do a few examples maybe that will help you solve the general case for leaving n unknown and solving for it.