Answer to Question #190059 in Statistics and Probability for Aariana Moultrie

Question

Will scored 625 on the SAT math portion. The math portion of the SAT has an average of 508 and a standard deviation of 110. Stephanie scored 25 on her ACT math portion. The math portion of the ACT has an average of 21 and a standard deviation of 4.7. Find the z- score for each student. Which statement below describes the student that has the more impressive score and why?

Answer 1

Let X be the score on math portion of ACT

X~ Normal ( 21, 4.7)

Sabrina score, X= 25

z-score $=\dfrac{X-\mu}{\sigma} = \dfrac{25-21}{4.7} = 0.8510$

Let Y be the score on math portion of SAT

X~ Normal ( 508, 110)

Sabrina score, X= 625

z-score $=\dfrac{X-\mu}{\sigma} = \dfrac{625-508}{110} = 1.0639$

Since the z-score for the math portion in SAT (1.0639) is greater than the z-score for the math portion in ACT (0.8510). Thus Sabrina performed better in SAT.