To determine how many standard deviations a value is from the mean in a normal distribution, we use the z-score formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
Where:
- [tex]\( X \)[/tex] is the value we are interested in (in this case, 25)
- [tex]\( \mu \)[/tex] is the mean of the distribution (in this case, 15)
- [tex]\( \sigma \)[/tex] is the standard deviation (in this case, 4)
Let's apply these values to the formula to find the z-score:
[tex]\[ z = \frac{25 - 15}{4} \][/tex]
First, calculate the difference between the value and the mean:
[tex]\[ 25 - 15 = 10 \][/tex]
Next, divide this difference by the standard deviation:
[tex]\[ \frac{10}{4} = 2.5 \][/tex]
Therefore, the value 25 is [tex]\( 2.5 \)[/tex] standard deviations above the mean.
So the correct answer is:
[tex]\[ \boxed{2.5} \][/tex]
