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------------------------------------------------ Calculate the standard score of the given [tex]x[/tex] value, [tex]x = 59.1[/tex], where [tex]\mu = 66.9[/tex] and [tex]\sigma = 3.4[/tex]. Round your answer to two decimal places.

To calculate the standard score, also known as the z-score, we apply the formula:

[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]

where:
- [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.

In this specific case, we have:
- [tex]\( x = 59.1 \)[/tex]
- [tex]\( \mu = 66.9 \)[/tex]
- [tex]\( \sigma = 3.4 \)[/tex]

Substituting these values into the formula gives:

[tex]\[ z = \frac{59.1 - 66.9}{3.4} \][/tex]

Calculate the difference in the numerator:

[tex]\[ 59.1 - 66.9 = -7.8 \][/tex]

Now, divide by the standard deviation:

[tex]\[ z = \frac{-7.8}{3.4} \][/tex]

After performing the division:

[tex]\[ z \approx -2.29 \][/tex]

Therefore, the standard score, rounded to two decimal places, is [tex]\( -2.29 \)[/tex].