Calculating Normal Probabilities
1.
Identify µ the population mean and σ the population standard deviation.
2.
Write the probability statement in symbols.
3.
Draw a Normal curve and do the following:
a.
b.
c.
d.
4.
Draw a vertical line at the center of the curve and put the value of the mean, µ, on the number line.
Place a mark on the number line beneath the curve for each of the three standard deviations above and below the mean
Put the value for X, or both X's if two are given, on the number line under the curve at their approximate values.
Shade the area under the curve that corresponds to the probability area indicated by the probability statement.
Press the following on your TI-83.
2nd | DISTR and select 2:normalcdf(
This function takes four arguments as shown below:
normalcdf ( lower boundary, upper boundary, mean, SD )
5.
Enter the following separated by commas in the order given.
a. The X-value at the lower bound of the area under the curve.
b. The X-value at the upper bound of the area under the curve.
c. The value of the mean, µ.
d. The value of the standard deviation, σ .
Note: Use 1E99 for positive infinity, and -1E99 for negative infinity. For E, press 2nd EE (above the comma key).
Calculating the value of X when the probability is known
When the area under the curve, that is the probability, is known and the value of the observation X at either end of that cumulative
probability is desired, the inverse of the normal is used. However, the inverse normal function requires as its first argument the
percentile at which the X is located, which may not be the same number as the probability area given.
1.
Identify µ the population mean, σ the population standard deviation, and the given probability.
2.
Draw a Normal curve and do the following:
a.
b.
c.
3.
Draw a vertical line at the center of the curve and write 50% on the number line at that point.
Locate the point/s under the curve that correspond to the boundaries of the given probability area and shade that area.
At the boundary point/s on the number line, write the percentile/s representing the cumulative area from negative infinity
up to that point.
PRESS the following on your TI-83:
2nd | DISTR | 3: invNorm (
This function takes up to 3 arguments as shown below. The percentile of interest must be entered as a decimal number.
invNorm ( Percentile, mean, SD )
4.
Enter the following separated by commas in the order given.
a. The value of the percentile as a decimal.
b. The value of the mean, µ.
c. The value of the standard deviation, σ .
5.
Repeat steps 3 and 4 for the other percentile if you have more than one.
Note: Refer to the Probability Flow Chart for other applications using the Normal probability functions.