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, μ, σ)

where:

• probability: the significance level
• μ: population mean
• σ: population standard deviation

You can access this function on a TI-84 calculator by pressing 2nd and then pressing VARS. This will take you to a DISTR screen where you can then use 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 α = .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 α = .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 α = .05. What is the z-critical value that corresponds to this alpha level?

To find this critical value, we can use the formula 1 – α/2. In this case, we will use 1 – .05/2 = .975 for the probability:

The answer is z = 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