Respuesta :
The z-score corresponding to a sample mean of m = 69 is -0.167
In this problem, we have been given :
population mean (μ) = 70, standard deviation (σ) = 12, sample size (n) = 4, sample mean (m) = 69
We know that, the Z-score measures how many standard deviations the measure is from the mean.
Also, the formula when calculating the z-score of a sample with known population standard deviation is:
[tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
where z = standard score
μ = population mean
σ = population standard deviation
m = the sample mean
and [tex]\frac{\sigma}{\sqrt{n} }[/tex] is the Standard Error of the Mean for a Population
First we find the Standard Error of the Mean for a Population
σ /√n
= 12 / √4
= 12 / 2
= 6
So, the z-score would be,
⇒ [tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
⇒ [tex]Z=\frac{69-70}{6 }[/tex]
⇒ Z = -1/6
⇒ Z = -0.167
Therefore, the z-score corresponding to a sample mean of m = 69 is -0.167
Learn more about the z-score here:
https://brainly.com/question/14103836
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