Question 7 of 13, Step 2 of 2 Consider the value of $$ t $$ such that the area under the curve between - $$ |t| $$ and $$ |t| $$ equals 0.9 . Stesson: 8.2 Student's t-distrinuturn table. 2 : Assuming the degrees of freedom equals 5 , select the $$ t $$-value from the $$ t $$-distribution tablect

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1. The central area under the curve is given as $$0.90$$. This means that the combined area in both tails is:
   $$
   1 - 0.90 = 0.10
   $$
   
2. Since the t-distribution is symmetric, each tail has an area of:
   $$
   \frac{0.10}{2} = 0.05
   $$
   
3. Therefore, the value of $$ t $$ is such that:
   $$
   P(T \le t) = 1 - 0.05 = 0.95
   $$
   for a t-distribution with 5 degrees of freedom.

4. Consulting the Student's t-distribution table for 5 degrees of freedom, the $$ t $$-value corresponding to a cumulative probability of $$0.95$$ is approximately:
   $$
   t \approx 2.015
   $$
   
5. Thus, the value of $$ t $$ that satisfies the condition is:
   $$
   t \approx 2.015
   $$
The $$ t $$-value is approximately 2.015.

Question 7 of 13, Step 2 of 2 Consider the value of \( t \) such that the area under the curve between - \( |t| \) and \( |t| \) equals 0.9 . Stesson: 8.2 Student's t-distrinuturn table. 2 : Assuming the degrees of freedom equals 5 , select the \( t \)-value from the \( t \)-distribution tablect

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