Calculating a Standard Normal Probability or the Area Under the Standard Normal Curve

1. Finding :

The TI-83/84 is equiped with a built in function called normcdf (,). It computes which is the area under the standard normal curve between and .

To calculate P(-1 < z < 2), press 2nd VARS [DISTR], ARROW DOWN to select 2:normalcdf(, and then press ENTER.

 
 
 

After 2:normalcdf( type -1 2 ), and then press ENTER. See the results below.

 
 

To 4 decimal places, the P(-1 < z < 2) = 0.8186.


2. Finding P(z < 2):

To calculate this probablity, P(z < 2), 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 2). Then press ENTER.

 
 
 

To 4 decimal places, the P (z < 2) = 0.9772.


3. Finding P(z > 1):

To find P(z > 1) use the fact that P(z > 1) = P (1 < z < ). Using E99 for , we calculate normalcdf(1, E99). The result is shown below.

To 4 decimal places, the P (z > 1) = 0.1587.



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