# How to Calculate NormalCDF Probabilities in Excel

The NormalCDF function on a TI-83 or TI-84 calculator can be used to find the probability that a normally distributed random variable takes on a value in a certain 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 example, suppose a random variable is normally distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value between 48 and 52 can be calculated as:

normalcdf(48, 52, 50, 4) = 0.3829

We can replicate this answer in Excel by using the NORM.DIST() function, which uses the following syntax:

NORM.DIST(x, σ, μ, cumulative)

where:

• x = individual data value
• μ = population mean
• σ = population standard deviation
• cumulative = FALSE calculate  the PDF; TRUE calculates the CDF

The following examples show how to use this function in practice.

### Example 1: Probability Between Two Values

Suppose a random variable is normally distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value between 48 and 52 can be calculated as:

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

The following image shows how to perform this calculation in Excel: The probability turns out to be 0.3829.

### Example 2: Probability Less Than One Value

Suppose a random variable is normally distributed with a mean of 50 and a standard deviation of 4. The probability that a random variable takes on a value less than 48 can be calculated as:

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

The following image shows how to perform this calculation in Excel: The probability turns out to be 0.3085.

### Example 3: Probability Greater Than One Value

Suppose a random variable is normally 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 be calculated as:

```=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.