How do I go from a z-score to a percent?
ANSWER:
Our z-score does not automatically turn into a percent by multiplying by 100 and adding a percent sign. We must use the standard normal table to figure out the area and turn that into a percent!
We can go from the x – value to a z – score to the area / percent by using the table.
We can also go backwards! We can be given an area / percent then by using the table find the associated z – score and then figure out the corresponding to x – value. More on how to go backwards is in this Course FAQ post:
Looking at Problem 15-11 a Heights. You should have obtained z = -1.33. Remember you need to always round to 2 decimal places for z scores.
In this problem we are asked for the left tail area.
Using the standard normal table (in your book or on our Course Site) we look up the area of the left tail associated with z-value of -1.33.
The left tail area from the chart is
Left tail area = .0918
We multiply this by 100 % to get a percent.
Rounded to the nearest percent this is 9%.
(Right tail area and other problem types can be found on the Course FAQ!)