Answer:
[tex]\boxed {\boxed {\sf z=2.2}}[/tex]
Step-by-step explanation:
The z-score tells us how many standard deviations a value is away from the mean.
The formula is:
[tex]z=\frac{x- \overline{x}}{s}[/tex]
where x is the value, [tex]\overline {x}[/tex] is the mean, and s is the standard deviation.
We want to find the z-score for the score of an 83, the mean is 72, and the standard deviation is 5.
[tex]x=83 \\\overline {x}= 72 \\s=5[/tex]
Substitute the values into the formula.
[tex]z=\frac{83-72}{5}[/tex]
Solve the numerator.
[tex]z=\frac{11}{5}[/tex]
Divide.
[tex]z=2.2[/tex]
The z-score is 2.2, which means the score of 83 is 2.2 standard deviations above the mean.
