Anna, a business major, took final exams in both Microeconomics and Macroeconomics and scored 85 on both. Her roommate Megan, also taking both courses, scored 76 on the Micro exam and 95 on the Macro exam. Overall, student scores on the Micro exam had a mean of 84 and a standard deviation of 4, and the Macro scores had a mean of 75 and a standard deviation of 13. Which student's overall performance was better? Explain.

Anna's overall performance was better.

Step-by-step explanation:

Microeconomics:

Anna's Score = 85

Megan's Score = 76

Mean Score = 84

Standard deviation = 4

Macroeconomics:

Anna's Score = 85

Megan's Score = 95

Mean Score = 75

Standard deviation = 13

We will calculate the z-scores for both the students in both the subjects and then compare those values to see which student scored better overall. The z-score can be calculated by the formula:

z = (X -μ)/σ

where X = student's score

           μ = mean score

           σ = standard deviation

Anna's scores:

z(Micro) = (85-84)/4

             =1/4

z(Micro) = 0.25

z(Macro) = (85-75)/13

              = 10/13

z(Macro) = 0.769

Overall z-score = 0.25 + 0.769 = 1.019

Megan's scores:

z(Micro) = (76-84)/4

             = -8/4

z(Micro) = -2

z(Macro) = (95-75)/13

              = 20/13

z(Macro) = 1.54

Overall z-score = -2 + 1.54 = -0.46

Clearly, Anna performed better than Megan because the overall z-score for Megan is -0.46 which is much less than that of Anna (1.019). Megan's overall z-score is negative which means it lies below the mean while that of Anna lies above the mean test scores. So, we can conclude that Anna's overall performance was better.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116