Here are summary statistics for the weights of Pepsi in randomly selected cans: $$ \mathrm{n}=36, \overline{\mathrm{x}}=0.82414 \mathrm{lb}, \mathrm{s}=0.00572 \mathrm{lb} $$. Use a confidence level of $$ 95 \% $$ to complete parts (a) through (d) below. a. Identify the critical value $$ \mathrm{t}_{\alpha / 2} $$ used for finding the margin of error. $$ \mathrm{t}_{\alpha / 2}=\square $$ (Round to two decimal places as needed.)

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**Step 1.**  
Determine the degrees of freedom:  
$$
\text{df} = n - 1 = 36 - 1 = 35.
$$

**Step 2.**  
Since the confidence level is $$95\%$$, the significance level is  
$$
\alpha = 1 - 0.95 = 0.05.
$$  
The value for each tail in the t-distribution is  
$$
\frac{\alpha}{2} = \frac{0.05}{2} = 0.025.
$$

**Step 3.**  
Find the critical value $$ t_{\alpha/2} $$ using the t-distribution table for $$\text{df} = 35$$ at $$ \frac{\alpha}{2} = 0.025 $$. The table provides:  
$$
t_{0.025, 35} \approx 2.03.
$$

**Final Answer:**  
$$
t_{\alpha/2} = 2.03.
$$
$$ t_{\alpha/2} = 2.03 $$

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