Calculating a Normal Probability or the Area Under the Normal Curve
1.
Finding 
:
The
TI-83/84 is equiped with a built in function called 
.
It computes
which is the area under the standard normal curve between 
and
.
To
calculate P(50 < x < 70) when 
= 40 and 
=
9, press 2nd VARS [DISTR], ARROW DOWN to select 2:normalcdf(,
and then press ENTER.
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After 2:normalcdf( type
50
70
40
9 ), and then press ENTER. See the results below.
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To 4 decimal places, the P(50 < x < 70) = 0.1328.
2. Finding P(x < 70):
To
calculate this probablity, P(x
< 70) when
= 40 and =
9, we can use the above normalcdf function since 
.
Although we cannot enter 
as
it is not a number, entering a very small number in its place, such as 
=
-E99, will do.
Press 2nd VARS [DISTR], ARROW DOWN to select 2:normalcdf(, and
then press ENTER. Press 
then press 2nd
[EE] and type 99. Press
and type 70
40
9). Then press ENTER.
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To 4 decimal places, the P (x < 70) = 0.9997.
To
find P(x > 60) when
= 40 and =
9, use the fact that P(x > 60) = P (60 < x < 
).
Using E99 for ,
we calculate normalcdf(60, E99, 40, 9). The result is shown below.
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To 4 decimal places, the P (x > 60) = 0.0131.
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