Transcript Normal Distribution using the TI

Normal
Distribution
using 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 associated
with the given area
Area or Probability
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.
Between 2 scores
 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.
Below a score: <112
 This
would return the area under a
normal curve below 112 (to the left)
 Assumes
there is no data below -9999.
z-scores
A standard or z-score measures the distance
between each item and the mean in terms of
the number of standard deviations.
𝒙 − 𝒎𝒆𝒂𝒏
𝒛=
𝒔𝒕𝒅𝒆𝒗
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:
𝒛=
𝟏𝟏𝟐−𝟏𝟎𝟎
= 0.8
𝟏𝟓
Between 2 z-scores
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.
Below a z-score
Another way to find the cumulative area for
scores below 112, would be to first convert to a
z-score:
𝒛=
𝟏𝟏𝟐−𝟏𝟎𝟎
= 0.8
𝟏𝟓
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 is
The 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 is
The area Above the raw score of 112.
Inverse: invNorm()
The Inverse Function
While normalcdf( L,H,𝒙,s) returns an area or
probability given a Low and High bound,
the inverse function: invNorm(p,𝒙,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.
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.
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
invNorm()
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.
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.