Mean and Standard Deviation

Alphlax

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Sep 10, 2013
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I have to find out someones mark on a couple tests
Test 1: Mean=77 SD=3.9
Test 2: Mean=83 SD=3.9
Test 3: Mean=77 SD=7.4

If someone can show me how to do one of them I can probably do the rest.
I know there has to be something with a bell chart and 68% but not really sure of the formula or steps.

Thanks in advance

edit: I added 2x(3.9) to 77 and got 84.8% which was the answer
Then for test #2 I did 88-3.9 which was the answer, how does the adding and subtracting of standard deviations work like this?
 
Last edited:
I have to find out someones mark on a couple tests
Test 1: Mean=77 SD=3.9
Test 2: Mean=83 SD=3.9
Test 3: Mean=77 SD=7.4

If someone can show me how to do one of them I can probably do the rest.
I know there has to be something with a bell chart and 68% but not really sure of the formula or steps.

Thanks in advance

edit: I added 2x(3.9) to 77 and got 84.8% which was the answer Answer to what question?
Then for test #2 I did 88-3.9 which was the answer, how does the adding and subtracting of standard deviations work like this?
The empirical rule you are trying to remember is that 68% of a normal distribution lies within ±1 standard deviation of the mean. That leaves 16% in the lower tail (< mean-sigma) and 16% in the upper tail (> mean+sigma). But that doesn't appear to be what you used. What exactly was the question?

The difference between Test 1 and Test 2 is just the mean .. the shape remains the same, just shifted higher by 6.
The difference between Test 3 and test 1 is the standard deviation. The peak is not as high and the tails are longer.
 
A teacher is analyzing the calss results for three biology tests. Each set of marks is normally distributed.
Determine Oliver's marks on each test, given the information shown to the right (above)
 
A teacher is analyzing the calss results for three biology tests. Each set of marks is normally distributed.
Determine Oliver's marks on each test, given the information shown to the right (above)
I still don't see what you know about Oliver's grade - I just see the class averages. Perhaps you are expected to remember these points about the normal distribution:
a) 68% of the distribution is within ±1 sigma from the mean
b) 95% of the distribution is within ±2 sigma from the mean
c) 99.7% of the distribution is within ±3 sigma from the mean

If the answer to the first question is +2 sigma, the question might have said Oliver scored in the top 2.5%

If the answer to the 2nd question is -1 sigma, Oliver scored better than 16% of the class

You didn't show the third answer.
 
Test 3 was 99.2%

Yeah I didn't get the question either!
99.2% in the distribution given for Test 3 is
z = (99.2 - 77)/7.4 = 3.0 standard deviations above the mean.
Or, the other way around, if Oliver's score was 3 standard deviations above the mean, then his score was 99.2%

What they want you to take away from this exercise is the empirical rules for the normal distribution:
a) 68% of the distribution is within ±1 sigma from the mean
b) 95% of the distribution is within ±2 sigma from the mean
c) 99.7% of the distribution is within ±3 sigma from the mean
 
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