I tried:
$$P(-x < 10 - x < x) = 0.95 \Leftrightarrow \\ P(10-x <x) -P(10-x > -x) = 0.95 \Leftrightarrow \\ P(10 < 0) -P(10>0) = 0.95$$
This makes no sense? Why?
$\mu=10$ and the standard deviation is $2$.
I found this: link
I can see that the OP did basically what I did but did the standardization directly.Why does it work if done that way and doesn't work the way I did it?
For comparison, here's a problem that uses 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 the Z table, etc.. my question is, why is it that what I tried to do works here but not in the first problem?