Question

Due to normality, the formula for computing z is the same for a single data value, as it is
for an average of the data values for a sample group.

True or false ?

Answer 1

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 $s = \frac{\sigma}{\sqrt{n}}$, hence, the formula is:

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

While for a single value, it is:

$Z = \frac{X - \mu}{\sigma}$

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• 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 $s = \frac{\sigma}{\sqrt{n}}$.

Hence, the formulas are different, and for an average of the data values for a sample group it is:

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

A similar problem is given at https://brainly.com/question/24663213