The z-table is the cdf for the Normal Distribution. So it counts the total probability from Z = -3.6 up to X. So say find Z =< -1. You look at the table. But if you want to find Z > -1 you can do what you said. It’s the same as [1 - (Z =< -1)]. BUT! You can cut out some unneeded work and just say Z > -1 is the same as Z =< +1 and just look up the value for 1 on the z-table also. Hope that helped. More on reddit.com

I wanna know how come they’re different There's multiple ways of presenting the same information. I'd prefer if everyone just tabulated the cdf, personally, but authors keep trying to "make it easier" on the non-mathematical students, in an attempt to (very slightly) reduce the calculation steps for they assume is the most common calculation. What they do instead is muddy the water, resulting in at least six different kinds of z-table being out there. Feel lucky you only have to deal with two. Note that the first image shows a picture of what is tabulated, removing any doubt at a glance. It's the cdf, the probability (area under the pdf) between -∞ and z for positive z values. The second image is the probability (area) between 0 and z for positive z values. It is at each point 0.5 smaller than the first table (look at the tables and see for yourself; the first one is always the second one + 0.5) It looks like your textbook has shaded in the area corresponding to the second table but what it's showing is how the various parts of the distribution relate to the tabulated area (e.g. that the upper tail is 0.5 minus the tabulated value). when to use each You can use either for any purpose you use the other for; there's just a slight difference in the way you use it More on reddit.com

Larger positive z-scores are not "better," they're more extreme. Likewise, more negative z-scores are more extreme in the opposite direction. Z=0 is the average. So a small positive z-score, like 0.1, is slightly above average, and a small negative z-score, like -0.1 is a little below average. I hope this explains things. More on reddit.com

Draw a diagram from the context of the question! This will always help! There’s an example here in on my site (you’ll need an account to view the solution - but it may help) normal distribution question More on reddit.com