# How do you use the standard normal curve tables?

I was trying to work over a practice problem, and I know I am supposed to use the tables to solve this problem. But I have no idea which part to use where.

The question and the tables are given as follows:

I found an example where to find a problem like 2.2, to find the most, you take the number (105) and subtract the mean, and divide by the standard deviation. So (105-100)/5=1. And I assume thats the number on the left side of the table. But how do you know which number to use for the top of the table? The example I saw, used the 0.0 column. Is this something used for the "at most" type of problems? And would it be different for the other parts of the problem?

Thanks for any help you can provide. It's all very much appreciated.

• Add the number for the column and the number for the row for the value of $Z$. For example, .5359 in the last column of the first row corresponds to $Z = 0.09$.
– Null
Oct 23 '14 at 19:13
• Like you said in the question, subtract the mean and divide by the standard deviation.
– Null
Oct 23 '14 at 19:18
• Look at my first comment again.
– Null
Oct 23 '14 at 19:28
• Another example: 3rd row, 2nd column is .5832 and corresponds to $Z = 0.2 + 0.01 = 0.21$
– Null
Oct 23 '14 at 19:36
• Among the (relatively few) disadvantages of the use of scientific calculators in high school math, one is that there's no motivation for 11th-graders to learn how to look up values in trig tables and log tables. This is another example of that kind of function table. Oct 23 '14 at 20:06

Tables of functions in books are usually printed in a format like this. To look up a function value, you find a number at the head of a row and a number at the head of a column that add up to your desired value of $x,$ then find the value of $f(x)$ at the intersection of that row and column.
For example, to look up the cumulative distribution $\Phi(x)$ for $x=0.63$ in the table below, use the row and column highlighted in yellow. We find that $\Phi(0.63)=0.7357.$ For $x=1.76$ we follow the row and column highlighted in green to find that $\Phi(1.76)=0.9608.$
For values of $x$ between the values listed in the tables, we usually interpolate linearly. (The tables are generally written with enough digits of $x$ so that linear interpolation of the remaining digits is accurate enough.)