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.

Hi! I need Help!
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

Thank you!

Answer:

4.75

Step-by-step explanation: given x=5 inches Z-score =1 let 'X' be the variable in normal distribution z=+1 when x=5 inches.

The mean length of the pavers produced at Patty's Pavers is 4.75 inches. Thus, the correct option is C.

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,

[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]

Where Z is the Z-score,

X is the data point,

μ is the mean and σ is the standard variable.

The Z-score of +1 is,

(x-μ)/σ = 1

(5-μ)/σ = 1

5 - μ = σ

The Z-score of +2 is,

(5.25-μ)/σ = 2

(5.25 - μ)/σ = 2

5.25 - μ = 2σ

Substitute the value of the 'σ', therefore, standard deviation from the above,

5.25 - μ = 2(5 - μ)

5.25 - μ = 10 - 2μ

5.25 - 10 = -2μ + μ

μ = 4.75

Hence, the mean length of the pavers produced at Patty's Pavers is 4.75 inches. Thus, the correct option is C.

Learn more about Z-score:

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