Questions: The following contingency table compares student's ability in math to their interest in studying finance from a random sample of students at a particular business school. Ability in Math Low Average High ------------------------------------- Interest in Finance Low 60 33 12 Average 37 29 80 High 26 58 18 What percentage of students with a high interest in finance have an average ability in math? Give your answer as a percentage to one decimal place but without the % symbol.

Solution Steps

We have a contingency table that compares students' ability in math to their interest in studying finance. The relevant data is as follows:

\[ \begin{array}{c|c|c|c|} & \text{Low} & \text{Average} & \text{High} \\ \hline \text{Low} & 60 & 33 & 12 \\ \hline \text{Average} & 37 & 29 & 80 \\ \hline \text{High} & 26 & 58 & 18 \\ \hline \end{array} \]

To find the total number of students with a high interest in finance, we sum the values in the "High" row:

\[ \text{Total}_{\text{High}} = 26 + 58 + 18 = 102 \]

From the table, the number of students with a high interest in finance and average ability in math is:

\[ \text{Average}_{\text{High}} = 58 \]

The percentage of students with a high interest in finance who have an average ability in math is calculated as follows:

\[ \text{Percentage} = \left( \frac{\text{Average}_{\text{High}}}{\text{Total}_{\text{High}}} \right) \times 100 = \left( \frac{58}{102} \right) \times 100 \approx 56.8627451 \]

Rounding this to one decimal place gives:

\[ \text{Percentage} \approx 56.9 \]

Final Answer