Answer :
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].
[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].
