5.2. The Density Curve of the Normal Distribution http://www.ck12.org
First read the table to find the correct probability for the databelowthisz−score. We must first round thisz−score
to− 0 .53. This will slightly under-estimate the probability, but it is the best we can do using the table. The table
returns a value of 0.2981 as the area below thisz−score. Because the area under the density curve is equal to 1, we
can subtract this value from 1 to find the correct probability of about.7019.
What about valuesbetweentwoz−scores? While it is an interesting and worthwhile exercise to do this using a
table, it is so much simpler using software or a graphing calculator that we will leave this for one of the homework
exercises.
Using Graphing Calculators: The Normal CDF Command.
Your graphing calculator has already been programmed to calculate probabilities for a normal density curve using
what is called acumulative density functionorcdf. This is found in the distributions menu above the VARS key.
Press[2nd] [VARS],[2]to select thenormalcdf(command. normalcdf( lower bound, upper bound, mean,
standard deviation)
The command has been programmed so that if you do not specify a mean and standard deviation, it will default to
the standard normal curve withμ=0 andσ=1.
For example, enteringnormalcdf(− 1 , 1 )will specify the area within one standard deviation of the mean, which we
already know to be approximately 68%.