How To Use Normal Cdf

The NormalCDF function on a TI-83 or TI-84 figurer can be used to find the probability that a normally distributed random variable takes on a value in a sure range.

On a TI-83 or TI-84 calculator, this function uses the following syntax

normalcdf(lower, upper, μ, σ)

where:

lower = lower value of range
upper = upper value of range
μ= population mean
σ= population standard deviation

For instance, suppose a random variable is unremarkably distributed with a mean of fifty and a standard deviation of 4. The probability that a random variable takes on a value between 48 and 52 tin can be calculated as:

normalcdf(48, 52, l, four) = 0.3829

Nosotros can replicate this answer in Excel by using theNORM.DIST() function, which uses the post-obit syntax:

NORM.DIST(ten, σ, μ, cumulative)

where:

10 = individual data value
μ= population mean
σ= population standard deviation
cumulative =FALSE summate the PDF; TRUE calculates the CDF

The following examples testify how to employ this function in exercise.

Example 1: Probability Between Two Values

Suppose a random variable is normally distributed with a mean of 50 and a standard departure of four. The probability that a random variable takes on a value between 48 and 52 tin can be calculated equally:

            =NORM.DIST(52, 50, 4,              TRUE) - NORM.DIST(48, 50, iv,              Truthful)

The following prototype shows how to perform this adding in Excel:

NormalCDF function in Excel

The probability turns out to exist 0.3829.

Case two: Probability Less Than Ane Value

Suppose a random variable is normally distributed with a hateful of 50 and a standard departure of four. The probability that a random variable takes on a value less than 48 tin exist calculated as:

            =NORM.DIST(48, 50, 4,              TRUE)

The following paradigm shows how to perform this adding in Excel:

The probability turns out to be 0.3085.

Example three: Probability Greater Than 1 Value

Suppose a random variable is unremarkably distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value greater than 55 can exist calculated every bit:

            =1 - NORM.DIST(55, 50, 4,              True)

The following image shows how to perform this calculation in Excel:

The probability turns out to be 0.1056.

Boosted Resources

Y'all can likewise use this Normal CDF Calculator to automatically notice probabilities associated with a normal distribution.