Answer:
The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.
Step-by-step explanation:
Mean SAT scores = 1026
Standard Deviation = 209
Mean ACT score = 20.8
Standard Deviation = 4.8
We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.
The formula to calculate the z-score is:
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.
z-score for junior scoring 860 in SAT exam will be:
![z=\frac{860-1026}{209}=-7.59](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B860-1026%7D%7B209%7D%3D-7.59)
z-score for junior scoring 16 in ACT exam will be:
![z=\frac{16-20.8}{4.8}=-1](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B16-20.8%7D%7B4.8%7D%3D-1)
The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.