You have the responsibility of reviewing students who apply to your University and helping choose the most qualified applicants. Some students took the ACT and some took the SAT. You want to compare two students. Student A took the ACT and got a score of 24, while student B got an SAT score of 1100. The year they took their tests, the ACT had an average score of 20.8 and a standard deviation of 5.6, while the SAT had an average score of 1060 and standard deviation of 195. Looking at just these test scores, which student appears more qualified?

Student who took ACT appears to be more qualified.

Step-by-step explanation:

We are given that Student A took the ACT and got a score of 24, while student B got an SAT score of 1100.

The year they took their tests, the ACT had an average score of 20.8 and a standard deviation of 5.6, while the SAT had an average score of 1060 and standard deviation of 195.

We have to check which student appears more qualified.

We will do this by finding the z scores for both the students and the student with higher z score is considered to be more qualified.

The z score probability distribution for a normal distribution is given by;

                       Z =  ~ N(0,1)

where,   = average score

            = standard deviation

Let X = score of the student

For this student :  X = score of ACT = 24

                              = average score for ACT = 20.8

                              = standard deviation for ACT = 5.6

So, z score =  

                   =   = 0.571

Hence, the student who took ACT has a z score of 0.571.

For this student :  X = score of SAT = 1100

                              = average score for SAT = 1060

                              = standard deviation for SAT = 195

So, z score =  

                   =   = 0.205

Hence, the student who took SAT has a z score of 0.205.

Therefore, it is clear that the z score for ACT is higher than that of SAT which means that student who took ACT appears to be more qualified.

the answer is a

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: