Answer:
The z-score for an elementary school whose mean score was 1300 is 0.878
Step-by-step explanation:
The z-score can be calculated from the formula
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Where [tex]z[/tex] represents the z score
[tex]x[/tex] represents the score
[tex]\mu[/tex] is the mean
and [tex]\sigma[/tex] is the standard deviation
From the question,
Mean scores for elementary schools had 1228 and a standard deviation of 82, that is
[tex]\mu = 1228[/tex]
[tex]\sigma = 82[/tex]
To determine the z-score ([tex]z[/tex]) for an elementary school whose mean score was 1300, that is
[tex]x = 1300[/tex]
Hence, the z-score is
[tex]z = \frac{x - \mu}{\sigma}[/tex]
[tex]z = \frac{1300 - 1228}{82}[/tex]
[tex]z = \frac{72}{82}[/tex]
[tex]z = 0.878[/tex]
Hence, the z-score for an elementary school whose mean score was 1300 is 0.878.
