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?

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JeanaShupp JeanaShupp · Answer 1 · 2020-09-21T03:32:12+02:00

Answer: 650

Step-by-step explanation:

Formula for z-score : [tex]Z=\dfrac{X-mean}{\text{Standrad deviation}}[/tex]

, where X = random variable that follows normal distribution.

Given: ACT test are approximately normally distributed with a mean of 18 and a standard deviation of 6.

For X = 27

[tex]Z=\dfrac{27-18}{6}=\dfrac{9}{6}=\dfrac{3}{2}=1.5[/tex]

Also, SAT test are approximately normally distributed with a mean of 500 and a standard deviation of 100.

If z-score for both tests are same then,

[tex]1.5=\dfrac{X-500}{100}\\\\\Rightarrow\ 1.5\times100=X-500\\\\\Rightarrow\ X-500=150\\\\\Rightarrow\ X=150+500\\\\\Rightarrow\ X=650[/tex]

Hence, the required score in SAT test to get the same z-score = 650