Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
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
#SPJ4
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
