I tried:

$$ P (-x <10 – x <x) = 0.95 Leftrightarrow \

P (10-x

P (10 < 0) -P(10>0) = 0.95 $$

This makes no sense? Why?

$ mu = 10 $ and the standard deviation is $ 2 $.

I found this: link

I can see that the OP basically did what I did, but did the standardization directly. Why does it work if it's done that way and it doesn't work like I did?

For comparison, here is a problem using a standard normal curve:

$$ P (-z <Z <z) = 0.95 Leftrightarrow \

P (Z <z) -P (Z <-z) = 0.95 Leftrightarrow \

P (Z <z) – (1-P (Z <z)) = 0.95 Leftrightarrow \

2P (Z <z) -1 = 0.95 Leftrightarrow P (Z <z) = 0.975 $$

Then I look it up in table Z etc. My question is, why does what I tried to do work here but not in the first problem?