HON 180 Using a TI calculator or Excel to solve problems involving the normal curve
1. Percentage under a normal curve
TI Calculator:
On a TI calculator, you can calculate the percentage under a normal curve by using the
normalcdf function.
Press 2nd Distr . “Distr” is in the third row, the fourth button from the left. “Distr” stands for
“Distributions.” Then choose “normalcdf” and press Enter “normalcdf” stands for “normal
cumulative distribution function.”
Your screen will look like
normalcdf(
Now you need to fill in the arguments of the normalcdf command. The arguments are
normalcdf(left endpoint, right endpoint, mean, SD).
This command gives the area under the normal curve from the left endpoint to the right endpoint.
Often you want the area from negative infinity to a certain endpoint or the area from a certain
endpoint to positive infinity. On a TI calculator, you should enter the very large negative
number -1EE99 in place of negative infinity, and you should enter the very large number positive
1EE99 in place of positive infinity.
Examples. For US women ages 45-55, the mean total cholesterol level is 225 mg/dl with a
standard deviation of 44 mg/dl. The distribution follows the normal curve.
a. Approximately what is the percentage of the women in this age group with cholesterol
between 200 and 250 mg/dl?
TI answer: normalcdf(200, 250, 225, 44)
b. Approximately what is the percentage of the women in this age group with cholesterol
between above 300 mg/dl?
TI answer: normalcdf(300, 1E99, 225, 44)
c. Approximately what is the percentage of the women in this age group with cholesterol
below 180 mg/dl?
TI answer: normalcdf(-1E99,180, 225, 44)
Excel:
The Excel command to use is NORMDIST(x, mean, SD , true). This command gives the area
from negative infinity to x. The last argument determines whether the function returns the area
under the curve from negative infinity to x rather the height of the histogram at the point x. In
practice, we almost never are interested in the height of the histogram at a particular point, so the
fourth argument is invariable set to true.
Examples. For US women ages 45-55, the mean total cholesterol level is 225 mg/dl with a
standard deviation of 44 mg/dl. The distribution follows the normal curve.
a. Approximately what is the percentage of the women in this age group with cholesterol
between 200 and 250 mg/dl?
Excel answer: NORMDIST(250, 225, 44, TRUE) − NORMDIST(200, 225, 44, TRUE)
b. Approximately what is the percentage of the women in this age group with cholesterol
between above 300 mg/dl?
Excel answer: 1−NORMDIST(300, 225, 44, TRUE)
c. Approximately what is the percentage of the women in this age group with cholesterol
below 180 mg/dl?
Excel answer: NORMDIST(180, 225, 44, TRUE)
2. Percentile for a normal curve
TI Calculator:
On a TI calculator, you can calculate a percentile for normal curve using the invNorm
function.
Press 2nd Distr . Then choose “invNorm” and press Enter “invNorm” stands for “inverse
cumulative density for the normal distribution ”
Your screen will look like
invNorm(
The arguments are
invNorm(percentile rank, mean, SD).
Examples. For US women ages 45-55, the mean total cholesterol level is 225 mg/dl with a
standard deviation of 44 mg/dl. The distribution follows the normal curve.
a. The lowest 30% of women in this a group have cholesterol level less than or equal to
____________.
Answer. invNorm(0.3, 225, 44)
b. The highest 25% of women in this group have cholesterol level greater than or equal to
____________.
Answer. invNorm(0.75, 225, 44)
Excel:
The Excel command to use is NORMINV(percentile rank, mean, SD). Exactly analogous to
the TI command, NORMINV gives the percentile with rank p, i.e., the value x so that the area of
the curve from negative infinity to x under the curve is p.
Examples. For US women ages 45-55, the mean total cholesterol level is 225 mg/dl with a
standard deviation of 44 mg/dl. The distribution follows the normal curve.
c. The lowest 30% of women in this a group have cholesterol level less than or equal to
____________.
Answer. NORMINV(0.3, 225, 44)
d. The highest 25% of women in this group have cholesterol level greater than or equal to
____________.
Answer. NORMINV(0.75, 225, 44)