Question 1152526
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Amanda's raw score is x = 680
The population mean of all SAT math scores is mu = 515
The population standard deviation of SAT math scores is sigma = 114


The z score for Amanda is
z = (x-mu)/sigma
z = (680-515)/114
z = 1.44736842105263
z = 1.45
Which is approximate.


Now let's find Pete's z score. 
His raw score is x = 27
The mean of all the ACT math scores is mu = 21
The standard deviation of all the ACT math scores is sigma = 5.1


His z score is
z = (x-mu)/sigma
z = (27-21)/5.1
z = 1.1764705882353
z = 1.18



Summary:
Amanda's z score is roughly z = 1.45
Pete's z score is roughly z = 1.18
Amanda has a higher z score, so she did better in her group compared to Pete's performance in his group (assuming both tests are effectively the same).
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