FRAME 62.
To find the area for z = 1.67, find 1.67 in the perimeter of the table. The units and tenths
digits (1.6) determine the row and the hundredths digit (.07) determines the column. The value at
the intersection (.4525) is the area under the curve for a distance 1.67 standard deviations above
the mean. The diagram below demonstrates how the area was found:
z
0
1
2
3
4
5
6
7
0.0
*
*
*
*
*
*
*
*
*
*
*
1.6
.4452
.4463
.4474
.4484
*
*
*
.4525
In a similar manner we would find the area under the normal curve from the mean to z = 2.51 to
be .4940. Find 2.51 in the perimeter of the table and, at the intersection of the 2.5 row and .01
column, read the area .4940. If the value of z is negative, it simply means the area is to the left of
the mean. We can ignore the sign and find the area under the curve as before. To preclude
interpolating between two z values, always round to two decimal points. The z value will be
rounded up if it is 5 or greater, or rounded down if it is 4 or less. Indicated below are examples
of rounding the z value.
Original z Value
Rounded
Area
1.2340
1.23
.3907
1.6667
1.67
.4525
2.4934
2.49
.4936
The normal curve table gives areas under the curve for a number of standard deviations (z's)
measured from the mean.
FRAME 63.
Find the areas under the curve associated with the following values for z:
a. 1.34
b. 2.69
c. 1.00
d. 3.00
e. -.09
93
FI0921
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