To find the area to the left of $-1.21$ under the t-distribution with 5 degrees of freedom, we use the cumulative distribution function (CDF) of the t-distribution.

Let's calculate this area.The area to the left of $-1.21$ under the t-distribution with 5 degrees of freedom is approximately $0.1402$.

Would you like more details or have any questions?

Here are some related questions:

1. What is the t-distribution used for in hypothesis testing?
2. How does the t-distribution compare to the normal distribution for small sample sizes?
3. What does a negative t-value indicate in the context of t-distributions?
4. How do degrees of freedom affect the t-distribution's spread?
5. What is the probability density function (PDF) in statistics?
6. How do you interpret the area under the curve in a t-distribution?
7. What is the difference between one-tailed and two-tailed tests in t-distributions?
8. How can you calculate critical t-values for different confidence levels?

Tip: When working with t-distributions, ensure the sample size and the assumptions of normality are met for accurate results.