Judging by your answers, you’re using a table that shows the area to the left of a given value of $z$. Your first answer is right: using a $4$-place table, I make it
$z=0.9772-0.8413=0.1359\;.$
You seem to have misplaced the decimal point for $y$: I get $0.023$ to three decimal places, or $0.02275$ to four significant figures.
For $w$ you seem to have taken the area to the left of the cutoff 3 instead of to the right: you want $w=1-0.999=0.001$ (actually about $0.001350$). Remember, the table is giving you everything to the left of a given cutoff; if you’re interested in $X\ge \text{ some cutoff}$, you need to subtract the table value from $1$ to get the area to the right of the cutoff.
For $x$ you want the table value at $4$ minus the table value at $-3$; I don’t know how many places your table gives, but that’s about
$0.99996833-0.001350=0.99861833\;;$
it appears that you have about half the right value, so you may be using a one-sided table and not compensating properly.
Most people find it helpful to make a rough sketch of the normal curve and mark the cutoff(s) of interest. For $x$, for instance, they would be $-3$ and $4$. Then figure out how to get the area to the left of $4$ and the area to the left of $-3$, and then subtract the latter from the former.
The applet here may be helpful: you can set it to show areas to the left of a cutoff (Up to Z
), to the right of a cutoff (Z onwards
), or from the centre at $0$ up to some positive cutoff (0 to Z
).