Question

If a sample of n = 4 scores is obtained from a normal population with µ = 70 and σ = 12. What is the z-score corresponding to a sample mean of m = 69?

Answer 1

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:

$Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }$

where z = standard score

μ = population mean

σ = population standard deviation

m = the sample mean

and $\frac{\sigma}{\sqrt{n} }$ 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,

⇒ $Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }$

⇒ $Z=\frac{69-70}{6 }$

⇒ 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:

brainly.com/question/14103836

#SPJ4