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You can use the **invNorm()** function on a TI-84 calculator to find z critical values associated with the normal distribution.

This function uses the following syntax:

**invNorm(probability, Î¼, Ïƒ)**

where:

**probability:**the significance level**Î¼:**Â population mean**Ïƒ:**population standard deviation

You can access this function onÂ a TI-84 calculator by pressingÂ 2nd and then pressingÂ VARS. This will take you to aÂ **DISTRÂ **screen where you can then useÂ **invNorm()**:

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

**Example 1: Z-Critical Value for One-Tailed Tests**

Suppose a researcher is conducting a left-tailed hypothesis test using Î± = .05. What is the z-critical value that corresponds to this alpha level?

The answer is z = **-1.64485**.

Suppose a researcher is conducting a right-tailed hypothesis test using Î± = .05. What is the z-critical value that corresponds to this alpha level?

The answer is z = **1.64485**.

**Example 2: Z-Critical Value for Two-Tailed Tests**

Suppose a researcher is conduct a two-tailed hypothesis test using Î± = .05. What is the z-critical value that corresponds to this alpha level?

To find this critical value, we can use the formula 1 â€“ Î±/2. In this case, we will use 1 â€“ .05/2 = .975 for the probability:

The answer is z =Â **1.96**.

**Example 3: Z-Critical Value for Cut-Off Scores**

Suppose the scores on a particular exam are normally distributed with a mean of 70 and a standard deviation of 8. What score separates the top 10% from the rest?

The answer is **80.25**.

Suppose the heights of males in a particular city are normally distributed with a mean of 68 inches and a standard deviation of 4 inches. What height separates the bottom 25% from the rest?

The answer is **65.3 **inches.

**Additional Resources**

How to Calculate Binomial Probabilities on a TI-84 Calculator

How to Calculate Poisson Probabilities on a TI-84 Calculator

How to Calculate Geometric Probabilities on a TI-84 Calculator