A statistician wants to see the relationship between the t-distribution and the standard normal distribution. The standard normal distribution is a normal distribution that has the parameters of the mean = 0 and the standard deviation = 1. The t-distribution is said to approximate the standard normal distribution as the number of degrees of freedom of the t-distribution increases.

Choose Graph > Probability Distribution
Plot.

Select Two Distributions, then click OK.

From Distribution 1, select t.

In Degrees of
freedom, enter 1.

From Distribution 2, select Normal.

In Mean, enter 0. In Standard
deviation, enter 1.

Click OK.

Repeat steps 1–7, but in step 4, specify the t-distribution to have 30 degrees of freedom to create the second graph.

Interpret the results

With 1 degree of freedom, the t-distribution is similar in shape to the standard normal distribution; however, the t-distribution has larger tails. With 30 degrees of freedom, the t-distribution is approximately the same as the standard normal distribution.