Question

two language majors, anna and megan, took exams in two languages. anna scored 80 on the first exam and 90 on the second exam. megan scored 85 on the first exam and 81 on the second exam. overall, student scores on the first exam had a mean of 72 and a standard deviation of 3, and the second exam scores had a mean of 75 and a standard deviation of 4. to qualify for language honors, a major must maintain at least an 85 average across all language courses taken. a) which of anna and megan qualify for language honors? a. only anna qualifies b. both anna and megan qualify c. only megan qualifies d. neither anna nor megan qualify b) which students overall performance was better?

Explanation:

Step1: Calculate Anna's average

Anna scored 80 on the first - language exam and 90 on the second - language exam. The average formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 2$, $x_1=80$ and $x_2 = 90$. So Anna's average is $\frac{80 + 90}{2}=\frac{170}{2}=85$.

Step2: Calculate Megan's average

Megan scored 85 on the first - language exam and 81 on the second - language exam. Using the average formula with $n = 2$, $x_1 = 85$ and $x_2=81$. Megan's average is $\frac{85+81}{2}=\frac{166}{2}=83$.

Step3: Determine who qualifies

Since a major must maintain at least an 85 average across all language courses taken, only Anna (with an average of 85) qualifies.

Step4: Compare overall performance

Anna's average is 85 and Megan's average is 83. So Anna's overall performance is better.

Answer:

a) A. Only Anna qualifies
b) A. Only Anna's overall performance was better