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.
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