Respuesta :
The z-scores of the monthly utility bills for the value of x as $60, $71 and $9 are -1.25, 0.125, and 2.25 respectively.
What is Z-score?
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.
As it is given that the standard deviation of the monthly utility bills is $8, while the mean is $70. Therefore, the z-score can be written as,
A.) X= 60
[tex]Z = \dfrac{X- \mu}{\sigma}=\dfrac{60- 70}{8} = -1.25[/tex]
B.) X = 71
[tex]Z = \dfrac{X- \mu}{\sigma} = \dfrac{71- 70}{8}=0.125[/tex]
C.) X = 92
[tex]Z = \dfrac{X- \mu}{\sigma}= \dfrac{92- 70}{8}=2.25[/tex]
Hence, the z-scores of the monthly utility bills for the value of x as $60, $71 and $9 are -1.25, 0.125, and 2.25 respectively.
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