- Save \& Exit Certify Lesson: 8.2 Student's t-Distribution Question 5 of 13, Step 1 of 2 Consider the value of \( t \) such that 0.025 of the area under the curve is to the right of \( t \). Step 1 of \( 2: \) Select the graph which best represents the given description of \( t \). Answer

The Student's t-distribution is a continuous probability distribution that arises in statistics when estimating population parameters when the sample size is small, and/or the population variance is unknown. This distribution is bell-shaped and symmetric, much like the normal distribution, but has heavier tails, which allow for more variability in smaller sample sizes—making it perfect for those "oops, I didn’t have a big enough sample!" moments when you're still striving for accuracy. To visualize the \( t \)-value with 0.025 of the area to the right, imagine your curve with a peak at the center and tails that stretch out more than in a regular bell curve. If you were to shade 2.5% of the area on the right, you would find that \( t \) lies toward the far right of the graph, marking it as a critical value for hypothesis testing—akin to a finish line that you hope your sample mean doesn’t cross when wrong!