Question 1085873: Use Appendix Table for Normal Distribution
to find area under Standard Normal Distribution curve
between z= -1 and z = 1
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Use a Standard Normal Table, or Z table, to find that
P(Z < -1.00) = 0.15866 (see note 1)
P(Z < 1.00) = 0.84134 (see note 2)
Once you know those two values, subtract them to get
P(-1.00 < Z < 1.00) = P(Z < 1.00) - P(Z < -1.00)
P(-1.00 < Z < 1.00) = 0.84134 - 0.15866
P(-1.00 < Z < 1.00) = 0.68268
So the final answer is approximately 0.68268
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Note 1: To find the value for P(Z < -1.00), you locate the row that starts with -1.0 (first page). This row is marked with a red rectangle in the image here. In that same image, the blue rectangle represents the column that has 0.00 up top. Combine the -1.0 row and 0.00 column to get the z value z = -1.00. The number 0.15866 in this row & column combo is the approximate area under the curve to the left of z = -1.00, which is why P(Z < -1.00) = 0.15866 approximately.
Note 2: Similar to note 1, we'll have this drawing done up where the red rectangle is everything in the row that starts with 1.0, and the blue rectangle represents everything in the column 0.00. The row and column combine to represent z = 1.00, in which the value 0.84134 is the area to the left of z = 1.00. So that's why P(Z < 1.00) = 0.84134 approximately.
Note 3: You can use an online tool such as this one to check your answer fairly quickly. Follow these steps:
Step 1) Make sure that Mean = 0
Step 2) Make sure that SD = 1
Step 3) Click the "between" radio button. In the two boxes type -1.00 and 1.00 in that order
Step 4) Hit the "recalculate" button
This is the result you should get. The page reports that the answer is approximately 0.6827 which is what we got earlier, just more accurate to one extra decimal place. In other words, 0.68268 rounded to 4 decimal places is 0.6827. The online web tool is also nice enough to throw in a sketch of the shaded area.
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