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.
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.