Both SAT and ACT are well-known placement tests that most US colleges require from Prospective students to be admitted in their programs.Scores in the SAT test are Approximately normally distributed with a mean of 500 and a standard deviation of 100.
Scores in the ACT test are approximately normally distributed with a mean of 18 and a Standard deviation of 6.What would be the score in the SAT test to get the same z-score as The admission requirement of an ACT score of 27?
A)500
B)550
C)600
D)650
E)700

Question

Quizplus · Accepted Answer

To find the SAT score that corresponds to the same z-score as an ACT score of 27, first calculate the z-score for the ACT score: $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For the ACT, $X = 27$, $\mu = 18$, and $\sigma = 6$, so $z = \frac{(27 - 18)}{6} = 1.5$. To find the corresponding SAT score, use the z-score with the SAT distribution: $X = \mu + z\sigma$, where $\mu = 500$ and $\sigma = 100$ for the SAT. Thus, $X = 500 + 1.5(100) = 500 + 150 = 650$.

Both SAT and ACT Are Well-Known Placement Tests That Most