Evaluate the formula $x^{2}=\frac{(n-1) s^{2}}{\sigma^{2}}$ when $\sigma=2.31, n=43$, and $s=3.82$ $x^{2}=\square$ (Round to three decimal places as needed.)

Step 1 ：Substitute the given values into the formula: \(x^{2} = \frac{(n-1) s^{2}}{\sigma^{2}}\)

Step 2 ：\(x^{2} = \frac{(43-1) * (3.82)^{2}}{(2.31)^{2}}\)

Step 3 ：Calculate the result: \(x^{2} = 114.8555686737505\)

Step 4 ：Round to three decimal places: \(x^{2} = 114.856\)

Step 5 ：Final Answer: \(x^{2} = \boxed{114.856}\)