Answered

In 2015, when she was a high school senior, Linda scored 680 on the mathematics part of the SAT. The distribution of SAT math scores in 2015 was Normal with mean 511 and standard deviation 120. Jack took the ACT and scored 26 on the mathematics portion. ACT math scores for 2015 were Normally distributed with mean 20. 8 and standard deviation 5. 4.


What is Linda's standardized score? (Enter your answer rounded to two decimal places. )


Linda’s standardized score=

Answer :

Answer:

1.41

Step-by-step explanation:

Since we are only focusing on Linda's SAT score, we only need to use the SAT distribution information.

We know that our mean is [tex]\mu=511[/tex] and our standard deviation is [tex]\sigma=120[/tex] with observed value [tex]x=680[/tex]

Our formula for the standardized score (also known as the z-score) is [tex]z=\frac{x-\mu}{\sigma}[/tex] which tells us how many standard deviations [tex]\sigma[/tex] above or below the mean [tex]\mu[/tex] the observed value of [tex]x[/tex] is:

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{680-511}{120}\\\\z\approx1.41[/tex]

Therefore, Linda's standardized score is 1.41, which means she scored 1.41 standard deviations above the mean.

Other Questions