SOLUTION: Amanda took the SAT and scored 680 on the mathematics part. The distribution of SAT math scores was Normal with mean 515 and standard deviation 114. Pete took the ACT and scored 27

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Question 1152526: Amanda took the SAT and scored 680 on the mathematics part. The distribution of SAT math scores was Normal with mean 515 and standard deviation 114. Pete took the ACT and scored 27 on the mathematics part. ACT math scores were Normally distributed with mean 21.0 and standard deviation 5.1.


a. Find the standardized (z) scores for both students.


b. Assuming that both tests measure the same kind of ability, who had the higher score? Explain your answer.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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).