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Calculate the standard score of the given X value, [tex]X = 35.8[/tex], where [tex]\mu = 29.4[/tex] and [tex]\sigma = 25.9[/tex]. Round your answer to two decimal places.

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.

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