From tech troubles to travel tips, IDNLearn.com has answers to all your questions. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

Calculate the following:

1. The probability of selecting at random a student who obtained a mark greater than the mean.
2. The probability of selecting at random a student who obtained a mark of 5 or 6.
3. The probability of selecting at random a student who obtained a mark less than 4.


Sagot :

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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.