Normal Distributions on the TI-83/84
The Normal Probability Distribution menu for the TI-83+/84+ is found under DISTR (2nd VARS).
NOTE: A mean of zero and a standard deviation of one are considered
to be the default values for a normal distribution on the calculator, if
you choose not to set these values.
The Normal Distribution functions:
#1: normalcdf cdf = Cumulative Distribution Function
It returns the percentage of area under a continuous distribution curve from a lower bound to an upper bound.
Syntax: normalcdf (lower bound, upper bound, mean, standard deviation)
#2: invNorm( inv = Inverse Normal Probability Distribution Function
This function returns the x-value given the probability region to the left of the x-value. (0 < area < 1 must be true.) The inverse normal probability distribution function will find the precise value
at a given percent based upon the mean and standard deviation.
Syntax: invNorm (probability, mean, standard deviation)
#3: normalpdf( pdf = Probability Density Function (HARDLY EVER USE)
This function returns the probability of a single value of the random variable x.
Use this to graph a normal curve. Using this function returns the y-coordinates of the normal curve.
Syntax: normalpdf (x, mean, standard deviation)
Example 1:
Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5. Find:
a) the probability that a value is between 65 and 80, inclusive.
b) the probability that a value is greater than or equal to 75.
b) the probability that a value is less than 62.
d) the 90th percentile for this distribution.
(answers will be rounded to the nearest thousandth)
1a: Find the probability that a value is between 65 and 80, inclusive. (This is accomplished by finding
the probability of the cumulative interval from 65 to 80.)
Syntax: normalcdf(lower bound, upper bound, mean, standard deviation)
CONTINUED
Answer:
1b: Find the probability that a value is greater than or equal to 75.
(The upper boundary in this problem will be positive infinity. The largest value the calculator can
handle is 1099. Type 10^99)
Answer:
1c: Find the probability that a value is less than 62.
(The lower boundary in this problem will be
negative infinity. To represent this, you’ll type in -10^99.)
Answer:
1d: Find the 90th percentile for this distribution.
(Given a probability region to the left of a value (i.e.,
a percentile), determine the value using invNorm.)
Answer:
For three more examples, go to my website under Normal Calculator Examples. It has answer for you.