**Instructions:** Compute critical z-values for the normal distribution probabilities using the form below. In order to do so, please type significance level \(\alpha\), and indicate the type of tail (left-tailed, right-tailed, or two-tailed)

## Z-Critical Values Calculator

Some more information about *critical values for the normal distribution probability*: First of all, critical values are points at the tail(s) of a certain distribution and the property of these values is that that the area under the curve for those points to the tails is equal to the given value of \(\alpha\). For a two-tailed case, the critical values correspond to two points to the left and right of the center of the distribution. They will have the property that the sum of the area under the curve for the left tail (from the left critical point) and the area under the curve for the right tail is equal to the given significance level \(\alpha\).

For a left-tailed case, the critical value corresponds to the point to the left of the center of the distribution. They will have the the property that the area under the curve for the left tail (from the critical point to the left) is equal to the given significance level \(\alpha\).

In the case of a right-tailed, the critical value corresponds to the point to the right of the center of the distribution. They will have the property that the area under the curve for the right tail (from the critical point to the right) is equal to the given significance level \(\alpha\)

The main properties are:

- If the distribution being analyzed is symmetric, the critical points for the two-tailed case are symmetric with respect to the center of the distribution
- For a symmetric distribution, finding critical values for a two-tailed test with a significance of \(\alpha\) is the same as finding one-tailed critical values for a significance of \(\alpha/2\).

Alternatively to using this calculator, you can use a z critical value table to find the values you need. Such tables typically come along with most Stats textbooks. It is indeed a good exercise to learn how to use those tables.

A similar type of critical value can be computed for the t-distribution. So use the following calculator if you need to compute critical t-values.

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