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Chapter
6
Continuous Random
Variables and the
Normal Distribution
Continuous random variables are used to approximate probabilities where there are many
possibilities or an infinite number of possibilities on a given trial. One of the most common
continuous distributions used to approximate probabilities is the normal distribution.
Traditionally normal distribution probabilities were figured using a normal distribution table.
The table method is being replaced with calculators such as the TI-83, TI-83 Plus, and TI-84
Plus. The calculator reduces the time needed to perform the calculations and reduces the
rounding errors that occur because of the brevity of the tables in elementary statistics textbooks.
Computing Normal Distribution Probabilities
The commands for computing probabilities of finding values that come from a normal
distribution are normalpdf( , normalcdf( , and invNorm( . They are located on the DISTR page
under the DISTR list. DISTR appears above the VARS key in the fourth row.
Standard Normal Distribution Probabilities
The function normalpdf( stands for normal probability density function and will approximate the
probability of getting a single value from a normally-distributed discrete population. Remember
the probability of getting any single value from a continuous distribution is zero since there are
an infinite number of possibilities. The values needed for the normalpdf( function are the
number, x , you are trying to find the probability of and the mean and standard deviation of the
normal distribution: normalpdf(x, µ, σ)
Example:
Find the probability of getting a 1 on the standard normal distribution. The mean and standard
deviation of the standard normal distribution are 0 and 1 respectively.
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