Patty's pavers has determined that a paver measuring 5 inches long has a z-score of +1 and a paver measuring 5.25 inches long has a z-score of +2.
what is the mean length of the pavers produced at patty's pavers?
4.25 inches
5.25 inches
4.75 inches
5.75 inches

The mean length of the pavers is 4.75 inches ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- A paver measuring 5 inches long has a z-score of +1

- A paver measuring 5.25 inches long has a z-score of +2

- The rule of z-score is ⇒ z = = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

∵ z = +1 when x = 5 inches

∴ 1 = (5 - μ)/σ

- Multiply both sides by σ

∴ σ = 5 - μ  

- Add μ to both sides

∴ σ + μ = 5 ⇒ (1)

∵ z = +2 when x = 5.25 inches

∴ 2 = (5.25 - μ)/σ

- Multiply both sides by σ

∴ 2σ = 5.25 - μ  

- Add μ to both sides

∴ 2σ + μ = 5.25 ⇒ (2)

* Lets solve equations (1) and (2) to find σ

- Subtract equation (1) from equation (2)

∴ (2σ + μ ) - (σ + μ) = 5.25 - 5

∴ σ = 0.25

- Substitute the value of σ in equation (1) to find μ

∴ 0.25 + μ = 5

- Subtract 0.25 from both sides

∴ μ = 4.75

∵ μ is the mean length of the pavers

∴ The mean length of the pavers is 4.75 inches

4.75 or C or 3rd Option

step-by-step explanation: