Normal Distributionusing the TI-83 Graphing Calculator

To access the TI-83 functions for Normal Distributions

Press 2nd and VARS

The TI-83 provides three functions for Normal Distribution:

normalpdf( height of the curve

normalcdf( area under the curve

invNorm( score associatedwith the given area

Area under the Curve

normalcdf(low, high, mean, stdev)

Returns the area under the curve (aka: probability,

relative frequency)between the low and high scores.

Area or Probability

This would return the area under a normal curve between 112 and 122 for a distribution that has a mean of 100 and a standard deviation of 15.

Between 2 scores

This would return the area under a normal curve below 112 (to the left)

Assumes there is no data below -9999.

Below a score: <112

A standard or z-score measures the distance between each item and the mean in terms of the number of standard deviations.

z-scores

The z-score based on a raw score of 112 for a distribution that has a mean of 100 and a standard deviation of 15 would be:

= 0.8

The normalcdf function defaults to a mean of zero and a standard deviation of one: these are the parameters for the standard normal distribution.

Between 2 z-scores

This would return the area under a standard normal curve between the z-scores of -1.5 and 2.

Between 2 z-scores

Below a z-score

Another way to find the cumulative area for scores below 112, would be to first convert to a z-score:

= 0.8

Find the area in the standard normal distribution. Since there is very little data more than 3.5 standard deviations below the mean, use any z-score below -3.5 as the low bound:

Normalcdf(-5,0.8)Would return the area below z=0.8, which isThe area below the raw score of 112.

Above a z-score

To find the area ABOVE 112, you could subtract the area below 112 from 1. The total area under the curve = 1. (Total probability = 100%)

OR use any z-score ABOVE 3.5 as the upper bound:

Normalcdf(0.8, 5)Would return the area ABOVE z=0.8, which isThe area Above the raw score of 112.

The Inverse FunctionWhile normalcdf( L,H,,s) returns an area or probability given a Low and High bound, the inverse function: invNorm(p,,s) returns a High bound when given a probability.

Like normalcdf( L,H) , invNorm(p) uses a default mean of zero and standard deviation of one: for the standard normal distribution.

Inverse: invNorm()

This invNorm() function would return the score associated with the 90th percentile.90% of the data would fall below this score and 90% of the area under the curve would be to the left of this Raw score.

invNorm()

Note: When you want the Raw score, enter values for mean and standard deviation. The default is to use the standard normal distribution – and to return a z-score

This invNorm(.25) function would return the z-score associated with the 25th percentile.25% of the data would fall below this score and 25% of the area under the curve would be to the left of this z-score.

invNorm()

Note that 75% of the data would fall ABOVE this score and 75% of the area under the curve would be to the RIGHT of this z-score.