Working with Probability Models
1. The Normal Model
We can use STATA to calculate similar values to those found in the Normal Table in the back of
the book. Suppose we want to find the proportion of the area under the normal curve that lies
below 1=z. To find this area we type
display normprob(1)
in the command window. This gives us the result .84134475, which you can verify coincides with
the value in the back of the book.
If, instead, we want to find the proportion of the area under the normal curve that lies above
1=z, we would need to type
display 1-normprob(1)
Suppose we want to know how many standard deviations above the mean we need to be in order
to lie in the 90th percentile of the normal curve. To find this value type
display invnorm(0.9)
Using this command, we find that that the corresponding z-value is equal to 1.2815516. In other
words, we need to be 1.28 standard deviations above the mean to be in the 90th percentile.
Ex. The height of U.S. men (in inches) approximately follows a normal model with mean 69.1
and standard deviation 2.9. Let X be the height of a randomly sampled man.
Suppose we want to estimate the probability that a man is between 5'6" and 6'. Then we can
simply type
display normprob((72-69.1)/2.9)-normprob((66-69.1)/2.9)
which gives us the result .69880214, or approximately 70% of all U.S. men are between 5'6" and
6'. Note that we, in this example, needed to insert the z-score into our calculations.
Suppose we want to know what is the shortest a man can be and still be in the top 10% of all U.S.
males. We can calculate this value by first finding how many standard deviations, z, above the
mean we need to be in order to be in the top 10%, and thereafter using the formula
µ
σ
+= z
x
to
find the proper value.
Doing these two tasks together we can write,
display invnorm(0.9)*2.9+69.1
This gives us the result 72.8165 inches.
