Question 1002005
If you don't want to use a calculator, then you must use a table. There is no other way to do this type of problem. It's nearly impossible to do by hand because it takes a very long time unless you're a human calculator.


I recommend a table like <a href = "https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf">this one</a>. Your stats textbook most likely has something like this in the back of the book. This table is the list of areas to the left of given z scores.


Note: some tables give areas to the right of z-scores so be careful how the table is set up. Read all the instructions for the table.


You have the correct z-score. It is z = -0.6


Look at the <a href = "https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf">table</a>. For this table I'm showing, you need to go to the row that starts with "-0.6" (towards the bottom of page 1). Then go to the column that has ".00" at the top. In this case, column 1. The intersection of the "-0.6" row and ".00" column has the number <font color=red>0.27425</font> in that cell


Recall that this table shows areas under the standard normal curve that are to the left of a given z score. The given z-score of -0.6 corresponds to the area of <font color=red>0.27425</font>


So that's another way to find the answer of <font color=red>0.27425</font>