VJesus12 wrote:For each student in a certain class, a teacher adjusted the student's test score using the formula y = 0.8x + 20, where x is the student's original test score and y is the student's adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?
A. 12
B. 16
C. 28
D. 36
E. 40
[spoiler]OA=B[/spoiler]
Source: Official Guide
Hi Vjesus12.
Before making any computation let's take into account the following result:
(1) If we add a number to all the data of a set \(S\), then the standard deviation of the set \(S\) doesn't change, that is to say, the standard deviation of the new data will be the same of the set \(S\).
(2) If we multiply all the data of a set \(S\) by a number \(k\), then the standard deviation of the new data will be the standard deviation of \(S\) multiplied by \(k\).
Now, we know that \(x\) represents the original test score of the students and \(y\) is the student's adjusted test score.
Since \(y=\color{green}{0.8}x+\color{red}{20}\) we can conclude, using the facts written above, that the standard deviation of the adjusted test scores of the students in the class is equal to the standard deviation of the original test score multiplied by \(\color{green}{0.8}\).
On the other hand, we are told that the standard deviation of the original test scores of the students in the class was 20. Then, the standard deviation of the adjusted test score is $$20\cdot0.8=16.$$ Therefore, the correct answer is the option
_B_.
I hope it is clear. <i class="em em-sunglasses"></i>
