To understand the concept of a z-score, we need to know that it measures the number of standard deviations a data point is from the mean of a distribution.
A z-score is calculated using the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where:
- [tex]\(X\)[/tex] is the value in the data set,
- [tex]\(\mu\)[/tex] is the mean of the data set,
- [tex]\(\sigma\)[/tex] is the standard deviation of the data set.
A z-score tells us how many standard deviations away from the mean a specific value lies.
Given a z-score of +1.6, it means the value lies 1.6 standard deviations above the mean.
Thus, a z-score of +1.6 directly represents a value that is 1.6 standard deviations above the mean.
Therefore, the correct answer to the question "A z-score of +1.6 represents a value which is how many standard deviations above the mean?" is:
[tex]\[ \boxed{1.6} \][/tex]
