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There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)?
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There are 75 students in a class and their average marks is 50 and S.D...
Calculation of Number of Students with More than 60 Marks
- Given, total number of students (n) = 75
- Average marks (μ) = 50
- S.D of marks (σ) = 5
- Formula for z-score = (X - μ) / σ
- For X = 60, z-score = (60 - 50) / 5 = 2
- Area under normal curve for z = 2 is 0.4772 (given)
- Formula for converting z-score to percentage = area under curve × 100
- Therefore, percentage of students who scored more than 60 = (1 - 0.4772) × 100 = 52.28%
- Number of students who scored more than 60 = percentage × total number of students = 52.28% × 75 = 39.21 ≈ 39 students
Explanation
To calculate the number of students who scored more than 60 marks, we first need to find the z-score for 60 marks using the formula (X - μ) / σ. Once we have the z-score, we can use the standard normal distribution table or calculator to find the area under the normal curve for that z-score. In this case, the area under the curve for z = 2 is given as 0.4772. This means that 47.72% of the students scored more than 60 marks.
However, we need to find the actual number of students who scored more than 60 marks. To do this, we need to convert the percentage to a number using the formula percentage × total number of students. The result is rounded off to the nearest whole number, which gives us 39 students.
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There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)?
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There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)?.
There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 75 students in a class and their average marks is 50 and S.D of marks is 5. Number of studentswho have secured more than 60 marks (Given that area under the normal curve for z = 2 is 0.4772)?.
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