Let's start by extracting and understanding the given data from the table. The table indicates the number of students who scored specific marks:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
\text{Marks scored} & 3 & 8 & 13 & 18 & 23 & 28 & 33 & 38 \\
\hline
\text{No. of Students} & 2 & 5 & 9 & 6 & 3 & 4 & 5 & 1 \\
\hline
\end{array}
\][/tex]
Total number of students:
[tex]\[ 2 + 5 + 9 + 6 + 3 + 4 + 5 + 1 = 35 \][/tex]
Let's calculate the probabilities for each part:
a) Marks greater than 28:
Students who scored greater than 28 are those who scored 33 or 38. The number of such students is [tex]\(5 + 1 = 6\)[/tex].
Probability (P) is given by:
[tex]\[ \text{P(marks > 28)} = \frac{\text{Number of students who scored more than 28}}{\text{Total number of students}} = \frac{6}{35} \approx 0.1714 \][/tex]
b) Marks less than 28:
Students who scored less than 28 are those who scored 3, 8, 13, 18, or 23. The number of such students is [tex]\(2 + 5 + 9 + 6 + 3 = 25\)[/tex].
Probability (P) is given by:
[tex]\[ \text{P(marks < 28)} = \frac{\text{Number of students who scored less than 28}}{\text{Total number of students}} = \frac{25}{35} \approx 0.7143 \][/tex]
c) Scored 33 marks:
The number of students who scored exactly 33 marks is [tex]\(5\)[/tex].
Probability (P) is given by:
[tex]\[ \text{P(marks = 33)} = \frac{\text{Number of students who scored 33}}{\text{Total number of students}} = \frac{5}{35} \approx 0.1429 \][/tex]
d) Between 3 and 33 marks (inclusive):
Students who scored between 3 and 33 marks include those who scored 3, 8, 13, 18, 23, 28, and 33. The number of such students is [tex]\(2 + 5 + 9 + 6 + 3 + 4 + 5 = 34\)[/tex].
Probability (P) is given by:
[tex]\[ \text{P(3 ≤ marks ≤ 33)} = \frac{\text{Number of students who scored between 3 and 33 (inclusive)}}{\text{Total number of students}} = \frac{34}{35} \approx 0.9714 \][/tex]
In summary, the probabilities are:
a) [tex]\( \approx 0.1714 \)[/tex]
b) [tex]\( \approx 0.7143 \)[/tex]
c) [tex]\( \approx 0.1429 \)[/tex]
d) [tex]\( \approx 0.9714 \)[/tex]
