A class of 43 students took an exam. They had a mean average of 67 and a standard deviation of 7.
a) how many students got a c
b) how many students got a b
c) what is a scoree needed to get an a
is a) 4 b) 1 c) 90
To find the answers to these questions, we first need to understand how grades are typically assigned based on the mean average and standard deviation of the class scores. Let's break it down step by step.
a) Finding the number of students with a grade of C:
To determine the number of students who received a C grade, we need to know the grading scale and the distribution of scores. Typically, a C grade corresponds to an average score that falls within one standard deviation below and above the mean.
In this case, since the mean average is 67 and the standard deviation is 7, one standard deviation below the mean would be 67 - 7 = 60, and one standard deviation above the mean would be 67 + 7 = 74.
Since the C grade range is within one standard deviation from the mean, we can calculate the percentage of students who fall within this range and then find the number of students. To do this, we can use the z-score formula.
Z-score = (Score - Mean) / Standard Deviation
For the lower bound of the C grade, the z-score would be (60 - 67) / 7 = -1.
For the upper bound of the C grade, the z-score would be (74 - 67) / 7 = 1.
Using a standard normal distribution table or a calculator to find the area under the curve between -1 and 1 (which represents the percentage of students who fall between the lower and upper bound), we get approximately 0.6827.
Therefore, the number of students who received a C grade would be 0.6827 * 43 = 29.4, which rounds to 29.
So, the answer to question a) is 29.
b) Finding the number of students with a grade of B:
To determine the number of students who received a B grade, we need to consider the range that corresponds to the B grade. Generally, a B grade falls within one standard deviation above the mean to two standard deviations above the mean.
Using the same calculations as before, one standard deviation above the mean is 67 + 7 = 74. So, two standard deviations above the mean would be 74 + 7 = 81.
We need to find the percentage of students who fall within this range. Similar to the calculations for the C grade, we can utilize the z-score formula.
For the lower bound of the B grade, the z-score would be (74 - 67) / 7 = 1.
For the upper bound of the B grade, the z-score would be (81 - 67) / 7 = 2.
Using the normal distribution table or a calculator to find the area under the curve between 1 and 2 (which represents the percentage of students who fall in this range), we get approximately 0.1359.
Therefore, the number of students who received a B grade would be 0.1359 * 43 = 5.85, which rounds to 6.
So, the answer to question b) is 6.
c) Finding the score needed to get an A:
To determine the score needed to get an A grade, we need to understand where it falls within the grading scale. An A grade is typically assigned to the highest tier of scores, which usually encompasses students who perform within two standard deviations above the mean.
Using the same calculations as before, two standard deviations above the mean is 67 + 7 + 7 = 81.
Therefore, the score needed to get an A grade would be 81 or higher.
So, the answer to question c) is 81.
To summarize:
a) The number of students who received a C grade is 29.
b) The number of students who received a B grade is 6.
c) The score needed to get an A grade is 81 or higher.