To find Brenda's [tex]$z$[/tex]-score given her height, we need to follow these steps:
1. Identify the given information:
- Brenda's height is 50 inches.
- We are provided with the mean height for 7-year-olds, which is 49 inches.
- The standard deviation of the heights is 2 inches.
2. Recall the formula for the [tex]$z$[/tex]-score:
[tex]\[
z = \frac{X - \mu}{\sigma}
\][/tex]
where:
- [tex]\( X \)[/tex] is the individual data point (Brenda's height).
- [tex]\( \mu \)[/tex] is the mean of the data set.
- [tex]\( \sigma \)[/tex] is the standard deviation of the data set.
3. Substitute the given values into the formula:
[tex]\[
z = \frac{50 - 49}{2}
\][/tex]
4. Perform the calculation:
[tex]\[
z = \frac{1}{2} = 0.5
\][/tex]
Therefore, Brenda's [tex]$z$[/tex]-score is 0.5.
