To determine how many standard deviations above the mean a value with a z-score of +1.6 is, we need to understand what a z-score represents. A z-score, also known as a standard score, indicates how many standard deviations a particular value is from the mean of the distribution.
A z-score is calculated using the formula:
[tex]\[ z = \frac{(X - \mu)}{\sigma} \][/tex]
where:
- [tex]\( X \)[/tex] is the value of the element,
- [tex]\( \mu \)[/tex] is the mean of the distribution,
- [tex]\( \sigma \)[/tex] is the standard deviation of the distribution.
A positive z-score indicates that the value is above the mean, and a negative z-score indicates that it is below the mean. The magnitude of the z-score tells us how many standard deviations the value is away from the mean.
In this case, a z-score of +1.6 means that the value is 1.6 standard deviations above the mean. Therefore, the correct answer is:
[tex]\[ 1.6 \][/tex]
So, a z-score of +1.6 represents a value which is 1.6 standard deviations above the mean.
