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?

650

Step-by-step explanation:

Formula for z-score :

, 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

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,

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

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x