t-distribution is a family of continuous probability distribution which arise when finding mean of normally distributed population. Observing the given figure, select the correct statement :

If degree of freedom is infinite, then t-distribution curve and normal distribution curve are exactly the same

The correct answer is Option (4) → If degree of freedom is infinite, then t-distribution curve and normal distribution curve are exactly the same

As the degree of freedom (v) of the t-distribution approach infinity (v → ∞), the t-distribution becomes identical to the standard normal distribution.

• Option 1: This is incorrect. The mean of a standard t-distribution is actually $0$ (it is symmetric around zero). The range of the distribution lies between $-\infty$ and $\infty$, but the mean is a specific point.

• Option 2: This is the opposite of the truth. As degrees of freedom increase (not decrease), the curve moves closer to the normal distribution. A lower $df$ means "heavier tails" and a flatter peak.

• Option 3: Incorrect. In the provided figure, Curve A (the tallest, narrowest curve) denotes the Standard Normal Distribution, while B and C represent t-distributions with lower degrees of freedom. The curve with the highest peak is always the one with the most degrees of freedom.