Let’s break down the solution step by step for each part of the question.
1. Mean Mark:
To find the mean mark, we add up all the marks and divide by the number of students.
The marks given are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Sum of the marks:
\(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55\)
Number of marks (students):
\(10\)
Mean mark:
\(\frac{55}{10} = 5.5\)
2. Probability of selecting a student who obtained a mark greater than the mean:
The mean is \(5.5\). We need to find the number of marks greater than \(5.5\) and divide by the total number of students.
Marks greater than \(5.5\) are: 6, 7, 8, 9, 10 (5 marks)
Probability:
\(\frac{5}{10} = 0.5\)
3. Probability of selecting a student who obtained a mark of 5 or 6:
The marks 5 or 6 are specifically asked.
Marks that are either 5 or 6: 5, 6 (2 marks)
Probability:
\(\frac{2}{10} = 0.2\)
4. Probability of selecting a student who obtained a mark less than 4:
We need to count the marks less than 4 and find their probability.
Marks less than 4 are: 1, 2, 3 (3 marks)
Probability:
\(\frac{3}{10} = 0.3\)
So, the solution is as follows:
- Mean mark: \(5.5\)
- Probability of selecting a student who obtained a mark greater than the mean: \(0.5\)
- Probability of selecting a student who obtained a mark of 5 or 6: \(0.2\)
- Probability of selecting a student who obtained a mark less than 4: [tex]\(0.3\)[/tex]
