Calculate the standard score of the given [tex]$X$[/tex] value, [tex]$X = 98.1$[/tex], where [tex]$\mu = 107.8$[/tex] and [tex]$\sigma = 106$[/tex]. Round your answer to two decimal places.

To calculate the standard score (also known as the z-score) for the given value [tex]$ X = 98.1 $[/tex], with a mean ([tex]$\mu$[/tex]) of 107.8 and a standard deviation ([tex]$\sigma$[/tex]) of 106, you can follow these steps:

1. Understand the Formula for the Z-score:
The z-score is calculated using the formula:
[tex]\[
z = \frac{X - \mu}{\sigma}
\][/tex]
Here:
- [tex]$ X $[/tex] is the value for which you want to find the z-score.
- [tex]$ \mu $[/tex] is the mean of the dataset.
- [tex]$ \sigma $[/tex] is the standard deviation of the dataset.

2. Plug in the Given Values:
Substitute the given numbers into the formula:
[tex]\[
z = \frac{98.1 - 107.8}{106}
\][/tex]

3. Calculate the Difference:
First, calculate the difference between [tex]$ X $[/tex] and [tex]$ \mu $[/tex]:
[tex]\[
98.1 - 107.8 = -9.7
\][/tex]

4. Divide by the Standard Deviation:
Next, divide the result by the standard deviation:
[tex]\[
z = \frac{-9.7}{106} \approx -0.09150943396226417
\][/tex]

5. Round the Result:
Finally, round the z-score to two decimal places:
[tex]\[
z \approx -0.09
\][/tex]

So, the standard score (z-score) for [tex]$ X = 98.1 $[/tex] is approximately [tex]$ -0.09 $[/tex].