A class of 43 students took an exam. Their mean grade average is 67 and standard deviation is 7.
a) how many students should get a C?
b) how many should get a B?
c) what score is necessary to get an A?
(pushed the post button too early)
the result you get will be a decimal between 0 and 1, the probability.
multiply that by the number of students, the 43
To solve these questions, we need to understand the grading scale based on the mean and standard deviation. Let's assume that the grading scale follows a normal distribution.
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Since the mean grade is 67 and the standard deviation is 7, we can infer that approximately 68% of the students scored between 60 (67-7) and 74 (67+7).
Now, let's breakdown each question:
a) To determine the number of students who should get a C, we need to calculate the percentage of students who fall within the range of a C grade. In most grading scales, a C grade typically falls within one standard deviation below the mean. Since we know that 68% of the students fall within one standard deviation, we can estimate that roughly 34% of the students (half of 68%) should get a C grade.
Therefore, the number of students who should get a C would be 34% of 43, which is approximately 14.62. Since we can't have a fraction of a student, we would round up to 15 students.
b) Similarly, to determine the number of students who should get a B, we need to calculate the percentage of students who fall within the range of a B grade. In most grading scales, a B grade typically falls within one standard deviation above the mean. Since we know that 68% of the students fall within one standard deviation, we can estimate that roughly 34% of the students (half of 68%) should get a B grade.
Therefore, the number of students who should get a B would be 34% of 43, which is approximately 14.62. Again, rounding up, we would have 15 students.
c) To find the score necessary to get an A, we need to determine which range of scores fall within one standard deviation above the mean. From our earlier calculations, we know that one standard deviation above the mean is 74. In most grading scales, an A grade typically falls in the high end of the distribution. Thus, we can consider a score of 75 or higher to be necessary to obtain an A in this case.
Keep in mind that these estimates are based on a normal distribution and assumptions about the grading scale. It is also possible that the actual grading scale used by the class or institution may differ, so it's always best to refer to the specific grading guidelines provided by the teacher or institution.
Here is an excellent applet that will do these kind of questions.
http://davidmlane.com/hyperstat/z_table.html
Unless I know what is considered a C in your country or region, I can't finish the problem for you
enter the mean, the standard deviation, then choose the "between" option
Enter the low end and the high end of your letter grade range.