Question 13 of 13 , Step 1 of 2 Consider the value of \( t \) such that the area to the left of \( -|t| \) plus the area to the right of \( |t| \) equals 0.05 . 8.2 student's t-Distribution Step 1 of 2 : Select the graph which best represents the given description of \( t \). Answer

\[ \textbf{Step 1: Graph Selection} \] The description indicates that we have a symmetric \( t \)-distribution with critical values at \( -|t| \) and \( |t| \), such that the combined area in the two tails is 0.05. Since the \( t \)-distribution is symmetric about 0, the left tail area (to the left of \( -|t| \)) is \[ \frac{0.05}{2} = 0.025, \] and similarly the right tail area (to the right of \( |t| \)) is \[ 0.025. \] Therefore, the graph that best represents this description is one where: - The curve is the standard \( t \)-distribution (symmetric and bell-shaped). - The areas in the far left (beyond \( -|t| \)) and the far right (beyond \( |t| \)) regions are shaded. - Each shaded tail has an area of 0.025. Select the graph showing a symmetric \( t \)-curve with shaded regions in both tails corresponding to extreme values beyond \( -|t| \) and \( |t| \).