The z-scores of the 68-95-99.7 rule aren't matching up with the values in my z-table

#1
The z-scores from the 68-95-99.7 rule, which are 1, 1.96 (or 2), and 3 according to my textbook, arent matching up with the values i get if i try to find them using the Z-table in the appendix of the textbook.

For example, the rule says 95% of the normal distribution falls within 1.96-2 std. devs. of the mean, while the value i get from the z-table is around 1.65. I'm pretty sure im using the table right but i get completely wrong values. Here's how i got that value


I also did a practice test and got most of the questions involving margin of error wrong. I'm pretty sure this is because I was using the z-table to calculate the critical values.

What am I doing wrong?
 

Dason

Ambassador to the humans
#2
Re: The z-scores of the 68-95-99.7 rule aren't matching up with the values in my z-ta

Note that the table gives you the area to the left of the z-score. This is ALL of the area to the left so this would even include the left most tail.