Questions: Evaluate the formula z = (x̄ - μ) / (σ / √n) when μ = 130, n = 12, x̄ = 134, and σ = 13.

Transcript text: Evaluate the formula $z=\\frac{\\bar{x}-\\mu}{\\frac{\\sigma}{\\sqrt{n}}}$ when $\\mu=130, n=12, \\bar{x}=134$, and $\\sigma=13$.

Solution

Solution Steps

Step 1: Identify the given values

Given values are sample mean ($ar{x}$) = 134, population mean ($\mu$) = 130, standard deviation ($\sigma$) = 13, sample size ($n$) = 12, and adjustment factor ($\Gamma$) = 1.

Step 2: Substitute the values into the formula

Substitute the values into the formula $z = \frac{ar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ with adjustment factor for $\sigma$, resulting in $z = \frac{ar{x} - \mu}{\frac{\sigma / \Gamma}{\sqrt{n}}}$.

Step 3: Simplify the expression and calculate the z-score

After substituting the values, we get $z = \frac{134 - 130}{\frac{13 / 1}{\sqrt{12}}}$. Simplifying this expression gives us the z-score as 1.07.