To determine the z-score of a given value in a data set, you can use the z-score formula:
[tex]\[ z = \frac{(X - \mu)}{\sigma} \][/tex]
Where:
- [tex]\( X \)[/tex] is the value in question (14.4 in this case)
- [tex]\( \mu \)[/tex] is the mean of the data set (24)
- [tex]\( \sigma \)[/tex] is the standard deviation of the data set (3)
Let's go through the steps:
1. Subtract the mean ([tex]\( \mu \)[/tex]) from the value ([tex]\( X \)[/tex]):
[tex]\[ 14.4 - 24 = -9.6 \][/tex]
2. Divide the result by the standard deviation ([tex]\( \sigma \)[/tex]):
[tex]\[ \frac{-9.6}{3} = -3.2 \][/tex]
Therefore, the z-score of 14.4 is [tex]\(-3.2\)[/tex].
The correct answer is:
d) -3.2
