For a class of 43 students, for a certain test, the mean grade is 67 and the standard deviation is 7.
a) how many students should receive a C?
b) how many students should receive a B?
c) what score would be necessary to obtain an A?
Nuts to this. Critieria for A, B, C is not something that is agreed to . Do you have some criteria for A, B, and C?
sorry that's all the question says. My teacher is weird she gives questions that say nothing and expects us to no what they mean.
To answer these questions, we need to understand the grading system based on the mean and standard deviation.
a) First, let's determine the grade range for a C. Generally, a C is a mediocre grade, so it would fall around the mean or slightly below. Usually, in a normal distribution, grades one standard deviation below the mean would correspond to a C.
The formula for calculating the z-score (a measure of how many standard deviations a data point is from the mean) is:
z = (x - mean) / standard deviation
To find the z-score corresponding to a C grade, which is one standard deviation below the mean, we substitute the values:
z = (X - 67) / 7
Solving for X when z = -1 (one standard deviation below the mean):
-1 = (X - 67) / 7
Multiply both sides by 7:
-7 = X - 67
Add 67 to both sides:
X = -7 + 67
X = 60
Therefore, any score below 60 would be considered a C. Now, we need to determine the number of students who should receive a C.
Let's assume that the distribution of grades follows a normal distribution, in which the percentage of students receiving a C is usually around 34%. One standard deviation below the mean should cover this 34% of students.
So, to find the number of students receiving a C:
Number of students receiving a C = 34% of total students
= 0.34 * 43
= 14.62 (approximately)
Since we can't have a fraction of a student, we can round up the result to determine that approximately 15 students should receive a C grade.
b) To find the number of students receiving a B, we look at the grade range for a B. A B is usually better than a C but not as good as an A. Typically, it falls between one standard deviation below the mean and the mean.
In a normal distribution, the percentage of students receiving a B is generally around 34% (between one standard deviation below the mean and the mean) as well. We can use the same approach as before to determine the number of students receiving a B:
Number of students receiving a B = 34% of total students
= 0.34 * 43
= 14.62 (approximately)
Since we can't have a fraction of a student, we can again round up the result to determine that approximately 15 students should receive a B grade.
c) Lastly, to determine the score necessary to obtain an A, we need to consider the grade range for an A. An A is usually considered excellent and falls above the mean.
In a normal distribution, the percentage of students receiving an A is typically around 68% (above one standard deviation from the mean). Since we want to find the cut-off score for an A, we need to determine the z-score that corresponds to the top 68% of students.
Using this formula:
z = (X - 67) / 7
We solve for X when z = 1 (one standard deviation above the mean):
1 = (X - 67) / 7
Multiply both sides by 7:
7 = X - 67
Add 67 to both sides:
X = 7 + 67
X = 74
Therefore, any score above 74 would be considered an A.