Questions: Help me solve this 2 parts remaining The following contingency table shows the distribution of grades earned by students taking a midterm exam in an MBA class, categorized by the number of hours the students spent studying for the exam. Complete parts a. and b. below. Click the icon to view the contingency table. Contingency table Grade Time Spent Studying A B C Less than 3 hours 4 16 10 3-5 hours 15 14 8 More than 5 hours 19 11 3

Help me solve this 2 parts remaining The following contingency table shows the distribution of grades earned by students taking a midterm exam in an MBA class, categorized by the number of hours the students spent studying for the exam. Complete parts a. and b. below. Click the icon to view the contingency table. Contingency table Grade Time Spent Studying A B C Less than 3 hours 4 16 10 3-5 hours 15 14 8 More than 5 hours 19 11 3
Transcript text: Help me solve this $\mid$ 2 parts remaining The following contingency table shows the distribution of grades earned by students taking a midterm exam in an MBA class, categorized by the number of hours the students spent studying for the exam. Complete parts a. and b. below. Click the icon to view the contingency table. Contingency table \begin{tabular}{|l|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & \multicolumn{3}{c|}{ Grade } \\ \hline Time Spent Studying & A & B & C \\ \hline Less than 3 hours & 4 & 16 & 10 \\ 3-5 hours & 15 & 14 & 8 \\ More than 5 hours & 19 & 11 & 3 \\ \hline \end{tabular}
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Solution

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Solution Steps

Solution Approach

To solve the problem, we need to analyze the given contingency table. The table provides the distribution of grades (A, B, C) based on the time spent studying. We can calculate the total number of students in each category and the overall distribution of grades. This will help us understand the relationship between study time and grades.

Step 1: Analyze the Contingency Table

The contingency table provides the distribution of grades based on the time spent studying. We have three categories for time spent studying: "Less than 3 hours", "3-5 hours", and "More than 5 hours". Each category has a distribution of grades A, B, and C.

Step 2: Calculate Total Students by Time Spent Studying

We calculate the total number of students in each time category:

  • Less than 3 hours: \(4 + 16 + 10 = 30\)
  • 3-5 hours: \(15 + 14 + 8 = 37\)
  • More than 5 hours: \(19 + 11 + 3 = 33\)
Step 3: Calculate Total Students by Grade

We calculate the total number of students for each grade:

  • Grade A: \(4 + 15 + 19 = 38\)
  • Grade B: \(16 + 14 + 11 = 41\)
  • Grade C: \(10 + 8 + 3 = 21\)
Step 4: Calculate Overall Total Number of Students

The overall total number of students is the sum of all students across all categories: \[ 30 + 37 + 33 = 100 \]

Final Answer

  • Total students by time spent studying: \(\{ \text{Less than 3 hours}: 30, \text{3-5 hours}: 37, \text{More than 5 hours}: 33 \}\)
  • Total students by grade: \(\{ \text{A}: 38, \text{B}: 41, \text{C}: 21 \}\)
  • Overall total number of students: \(\boxed{100}\)
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