Respuesta :
Using the Central Limit Theorem, the statement is false, as for the averages of the data values for a sample group, the standard error is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], hence, the formula is:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
While for a single value, it is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
Hence, the formulas are different, and for an average of the data values for a sample group it is:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
A similar problem is given at https://brainly.com/question/24663213
