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There are 75 questions in a class and their average marks are 50 and standard deviation of marks is 5. how many students have secured more than 60 marks?
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There are 75 questions in a class and their average marks are 50 and s...
Given Information:
- Total number of questions in the class: 75
- Average marks of the students: 50
- Standard deviation of marks: 5

Calculating the number of students who secured more than 60 marks:
To calculate the number of students who secured more than 60 marks, we need to find the percentage of students who scored more than 60 marks and then multiply it by the total number of students.

Step 1: Finding the z-score:
The z-score measures how many standard deviations an individual data point is from the mean. In this case, we can calculate the z-score for 60 marks as follows:

z = (x - μ) / σ

Where:
- x = 60 (marks)
- μ = 50 (average marks)
- σ = 5 (standard deviation)

Substituting the values, we get:

z = (60 - 50) / 5
z = 2

Step 2: Finding the percentage of students:
To find the percentage of students who scored more than 60 marks, we need to find the area under the normal distribution curve to the right of the z-score of 2. We can use a standard normal distribution table or a calculator to find this probability.

According to the standard normal distribution table, the area to the left of a z-score of 2 is approximately 0.9772. Therefore, the area to the right of 2 is 1 - 0.9772 = 0.0228 or 2.28%.

Step 3: Calculating the number of students:
To calculate the number of students who secured more than 60 marks, we multiply the percentage (2.28%) by the total number of students (75).

Number of students = 0.0228 * 75
Number of students = 1.71

Conclusion:
Approximately 1.71 students have secured more than 60 marks in the class. Since we cannot have a fraction of a student, we can round up the number to the nearest whole number. Therefore, we can conclude that 2 students have secured more than 60 marks.
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There are 75 questions in a class and their average marks are 50 and standard deviation of marks is 5. how many students have secured more than 60 marks?
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