Answer :
To calculate the standard score, also known as the z-score, we need to use the following formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where:
- [tex]\( X \)[/tex] is the given value, which is 35.8 in this case.
- [tex]\( \mu \)[/tex] is the mean, given as 29.4.
- [tex]\( \sigma \)[/tex] is the standard deviation, given as 25.9.
Now let's substitute these values into the formula:
1. Subtract the mean ([tex]\( \mu \)[/tex]) from the given value ([tex]\( X \)[/tex]):
[tex]\[
X - \mu = 35.8 - 29.4 = 6.4
\][/tex]
2. Divide the result by the standard deviation ([tex]\( \sigma \)[/tex]):
[tex]\[
z = \frac{6.4}{25.9} \approx 0.24710424710424705
\][/tex]
3. Finally, round the z-score to two decimal places:
[tex]\[
z \approx 0.25
\][/tex]
Thus, the standard score (z-score) for the given X value is approximately 0.25.
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where:
- [tex]\( X \)[/tex] is the given value, which is 35.8 in this case.
- [tex]\( \mu \)[/tex] is the mean, given as 29.4.
- [tex]\( \sigma \)[/tex] is the standard deviation, given as 25.9.
Now let's substitute these values into the formula:
1. Subtract the mean ([tex]\( \mu \)[/tex]) from the given value ([tex]\( X \)[/tex]):
[tex]\[
X - \mu = 35.8 - 29.4 = 6.4
\][/tex]
2. Divide the result by the standard deviation ([tex]\( \sigma \)[/tex]):
[tex]\[
z = \frac{6.4}{25.9} \approx 0.24710424710424705
\][/tex]
3. Finally, round the z-score to two decimal places:
[tex]\[
z \approx 0.25
\][/tex]
Thus, the standard score (z-score) for the given X value is approximately 0.25.
