Question 220383:
Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What percent of students scored above 95 points? I got 18.6/6.1= 3.05 but what step do i do next? I'm lost after that.
What if the question were to ask Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What percent of students scored below 85 points? what would it be or look like then?
Thanks so much for your help!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mean is 76.4 and standard deviation is 6.1
You need a Z-table or Z-table calculator to show you what the values are.
Here's a Z-table calculator.
Z-Table Calculator
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With a mean of 76.4 and a Standard Deviation of 6.1, only .1147% of the students scored above 95.
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95 is more than 3 standard deviations above the mean (95-76.4)/6.1 = 3.049180328
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You were right about the standard deviations above the mean. I's approximately 3.05.
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You need the table or the calculator to show you what the percentage is.
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Click on the hyperlink to go to the Table Calculator.
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In the top graph, enter a mean of 76.4 and a Standard Deviation of 6.1
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Select Above and enter 95.
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It will show you Shaded area: 0.001147 which is 0.1147%.
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Go to the bottom graph.
Enter 0 for mean and 1 for Standard Deviation.
Enter .001147 in the box for Shaded Area.
Select Above.
It will tell you the Standard Deviations above the mean.
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The answer was 3.0493 which is close to what you calculated.
The 3.0493 is more accurate.
Actually 3.0491803428 is more accurate. There probably some rounding going on. The showed .001147 which was probably rounded.
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Go back to the top graph and enter 0 for the mean and 1 for the standard deviation.
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Select Above and enter 3.0493.
You'll get .001147 as your answer.
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Whether you used a mean of 76.4 and a standard deviation of 6.1, you will get the same answer as if you entered a man of 0 and a standard deviation of 1.
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This is not surprising since the Z-Table is calculated from the mean and standard deviation.
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To find the percentage of students that scored below 85%, do the following:
Go to the top graph.
Enter a mean of 76.4
Enter a Standard Deviation of 6.1
Select Below and enter 85
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Answer is .920706 which means that 92% of the students scored below 85.
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Go to the bottom graph.
Enter a mean of 0 and a standard deviation of 1.
Enter .920706 in the shaded area box.
Select Below.
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It tells you that 85 is 1.4098 standard deviations above the mean.
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Go back to the top graph.
Enter a mean of 0 and a standard deviation of 1.
Select Below.
Enter 1.4098 (It's above the mean so it's still positive.
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It will tell you that the Shaded area is .920706 which is the same answer you got when you entered a mean of 76.4 and a standard deviation of 6.1
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The Z table converts mean and standard deviation to mean of 0 and standard deviation of 1.
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The formula is Value minus mean divided by standard deviation.
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mean is 76.4
standard deviation is 6.1
When Value is 76.4, Z-Table Value is 0 (76.4-76.4)/6.1 = 0
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When Value is 95, Z-Table Value is (95-76.4)/6.1 = 3.04918.....
When Value is 85, Z-Table Value is (85-76.4)/6.1 = 1.409836...
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Percentages are taken from the table.
They usually tell you the percent to the left or to the right of your value.
If the table tells you to the right, you need to get 1 minus what the table tell you to get to the left.
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Calculator that I linked you to does it all for you.
You just tell it what you want.
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