Use of TI-83 Calculator to
Compute Normal Probability Distribution Values;
Compute the Value(s) Given an Area

Since z-scores are for the Standard Normal Distribution,
the syntax is normalcdf(smaller z, larger z).

Example (TI-83): Find the probability that a z-score is between -1.5 and 2. That is, find P(-1.5 ≤ z ≤ 2).

Find probability or area

Press 2nd VARS [DISTR].

Scroll down to

2:normalcdf(

Press ENTER.

Enter -1.5,2)

and press ENTER

to get the answer .91044.

The syntax is normalcdf(smaller z, larger z).

 

Since z-scores are for the Standard Normal Distribution,
the syntax is invNorm(area to left of desired z).

Example (TI-83): Find the z-score for an area of 0.25 to the left of the z-score.

 

Press 2nd VARS [DISTR].

Scroll down to

3:invNorm

Press ENTER.

Enter .25)

and press ENTER

to get the answer -.67.

The syntax is invNorm(area to left of desired z).

 

Since the IQs are NOT Standard Normal Distribution,
the syntax is normalcdf(smaller value, larger value, µ, σ).

Example (TI-83): Adult IQs are normally distributed with µ = 100 and σ = 15. Find the probability that a randomly selected IQ is less than 112. That is, find P(x < 112). Since this is a continuous function, we have P(x < 112) = P(x ≤ 112).

 

Press 2nd VARS [DISTR].

Scroll down to

2:normalcdf(

Press ENTER.

Enter -9999,112,100,15)
and press ENTER
to get the answer .7881.

The syntax is normalcdf(smaller, larger, µ, σ).

Note: The -9999 is used as the smaller value to be at least 5 standard deviations from the mean.

Find the probability that a randomly selected IQ is at least 122. That is, find P(x ≥ 122).

 

Press 2nd VARS [DISTR].

Scroll down to

2:normalcdf(

Press ENTER.

Enter 122,9999,100,15)
and press ENTER
to get the answer .0712.

The syntax is normalcdf(smaller, larger, µ, σ).

Note: The 9999 is used as the larger value to be at least 5 standard deviations from the mean.

Find the probability that a randomly selected IQ is between 112 and 122.
That is, find P(112 ≤ x ≤ 122).

 

Press 2nd VARS [DISTR].

Scroll down to

2:normalcdf(

Press ENTER.

Enter 112,122,100,15)

and press ENTER
to get the answer .1406.

The syntax is normalcdf(smaller, larger, µ, σ).