The correct answer is option 'A' - t-distribution. Let's understand why the t-distribution has a greater spread than the Normal distribution.

1. Understanding the Normal Distribution:
The Normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric and bell-shaped. It is defined by its mean (μ) and standard deviation (σ). The shape of the Normal distribution is determined solely by these two parameters.

2. Understanding the t-Distribution:
The t-distribution is also a continuous probability distribution, but it is wider and more spread out than the Normal distribution. It is characterized by its degrees of freedom (df), which determines the shape of the distribution. The degrees of freedom represent the sample size used to calculate the t-statistic.

3. Greater Spread of the t-Distribution:
The spread of a distribution can be measured by its standard deviation. For the Normal distribution, the standard deviation is fixed and is represented by σ. However, for the t-distribution, the standard deviation is not fixed and is instead estimated based on the sample size and the variability within the data.

Since the t-distribution is based on smaller sample sizes (represented by degrees of freedom), it has a larger uncertainty compared to the Normal distribution. This increased uncertainty results in a wider spread of the t-distribution compared to the Normal distribution.

4. Application of the t-Distribution:
The t-distribution is commonly used in statistical inference when dealing with smaller sample sizes. It is particularly useful when the population standard deviation is unknown and needs to be estimated from the sample.

The t-distribution allows for more variability in the data, accounting for the uncertainty introduced by smaller sample sizes. This makes it more appropriate for making inferences and constructing confidence intervals when working with limited data.

In summary, the t-distribution has a greater spread than the Normal distribution because it accounts for the increased uncertainty introduced by smaller sample sizes. The degree of spread in the t-distribution is determined by the degrees of freedom, which represent the sample size used to calculate the t-statistic.