Sophia took the gre and scored 160 on the verbal reasoning section and 157 on the quantitative reasoning section. the mean score of all test takers for the verbal reasoning section was 151 with a standard deviation of 7.00. the mean score of all test takers for the quantitative reasoning section was 153 with a standard deviation of 7.67. suppose that the distributions of both scores are approximately normal. what is the z-score for sophia's quantitative reasoning score?

answer: 5

step-by-step explanation:

since, the range is the difference between the lowest and highest values of the given sample space.

and, here the sample space = { 3, 1, 0, 4, 1, 4, 2, 3, 0, 5, 0, 1, 1, 2, 0, 4, 1,4, 4 ,2 ,3 ,2 ,0 ,1 ,4 }

here, the highest value of the given sample = 5

and, the lowest value = 0

therefore, the range of the sample space = 5 - 0 = 5

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.