eileen's energy bars has determined that an energy bar measuring 3.25 inches long has a z-score of +1 and an energy bar measuring 3.50 inches long has a z-score of +2.
what is the standard deviation of the length of energy bars produced at eileen's energy bars?
3.5
3.25
0.75
0.25

The standard deviation of the length of energy is 0.25 ⇒ 4th answer

Step-by-step explanation:

* Lets explain how to solve the problem

- An energy bar measuring 3.25 inches long has a z-score of +1

- An energy bar measuring 3.50 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 = 3.25 inches

∴ 1 = (3.25 - μ)/σ

- Multiply both sides by σ

∴ σ = 3.25 - μ  

- Add μ to both sides

∴ σ + μ = 3.25 ⇒ (1)

∵ z = +2 when x = 3.50 inches

∴ 2 = (3.50 - μ)/σ

- Multiply both sides by σ

∴ 2σ = 3.50 - μ  

- Add μ to both sides

∴ 2σ + μ = 3.50 ⇒ (2)

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

- Subtract equation (1) from equation (2)

∴ (2σ + μ ) - (σ + μ) = 3.50 - 3.25

∴ σ = 0.25

∵ σ is the standard deviation

∴ The standard deviation of the length of energy is 0.25

d

step-by-step explanation:

42.4

step-by-step explanation:

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