Question

Use the z -score formula, z=x−μσ , and the information below to

find the mean, μ . Round your answer to one decimal place, if
necessary. z=1.25 , x=21.3 , and σ=1.2

Answer 1

Using the z-score formula and rearranging it, the mean μ is found to be 19.8 when z=1.25, x=21.3, and σ=1.2.

Step-by-step explanation:

To find the mean μ using the z-score formula, we can rearrange the formula z = (x - μ) / σ to solve for μ. Given that z = 1.25, x = 21.3, and σ = 1.2, we can follow these steps:

• Multiply both sides of the z-score formula by σ to isolate (x - μ) on one side: 1.25 * 1.2 = (x - μ)
• Calculate the left side: 1.25 * 1.2 = 1.5
• Add μ to both sides to solve for the mean: x = 1.5 + μ
• Insert the value of x to find the mean: 21.3 = 1.5 + μ
• Subtract 1.5 from both sides to isolate the mean: μ = 21.3 - 1.5 = 19.8

Therefore, the mean is 19.8, rounded to one decimal place.