Question 944220: Some teachers grade “on a (bell) curve” based on the belief that classroom test scores are normally distributed. One way of doing this is to assign a “C” to all scores within one standard deviation of the mean. Then, the teacher would assign a “B” to all scores between one and two standard deviations above the mean, an “A” to all scores more than two standard deviations above the mean, and use symmetry to define the regions for “D” and “F” on the left side of the normal curve.
If 200 students take an exam, the number of students who would
receive a “B” is_____.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can use the rule of thumb for normal distribution to figure this out.
the rule is:
68% are within 1 standard deviation from the mean.
95% are within 2 standard deviations from the mean.
the difference between 95 and 68 are the percent that are between 1 and 2 standard deviations from the mean plus or minus.
the difference between 100% and 95% are the percent that are greater than 2 standard deviations from the mean plus or minus.
you will get:
68% are within 1 standard deviation from the mean.
95% - 68% = 27% are between 1 standard deviation and 2 standard deviations from the mean.
100% - 95% = 5% are beyond 2 standard deviations from the mean.
Since A and B are above the mean and D and F are below the mean, and since the distribution curve is symmetric, you will get:
68% will get a C because they are within 1 standard from the mean. Half of them will be above the mean and half of them will be below the mean.
13.5% will get a B because they are between 1 and 2 standard deviations above the mean.
13.5% will get a D because they are between 1 and 2 standard deviations below the mean.
2.5% will get an A because they are beyond 2 standard deviations above the mean.
2.5% will get an F because they are beyond 2 standard deviations below the mean.
Add up all the percentages and you get 68 + 2 * 13.5 + 2 * 2.5 = 100%.
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