Question 747511: Can someone help with the easy formula written out to solve these two:
Normal Distribution has a mean of 25, and standard deviation of 2.5. Use the 68-95-99.7 rule to find percentage of values in the distribution:
1. Between 20 and 30
AND
2. Between 25 and 32.5
Found 2 solutions by rothauserc, mikeebsc:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! We are asked:
Normal Distribution has a mean of 25, and standard deviation of 2.5. Use the 68-95-99.7 rule to find percentage of values in the distribution:
1. Between 20 and 30
AND
2. Between 25 and 32.5
The standardization or z-score formula is (value - mean)/standard deviation
1) z-score for 30 is (30-25)/2.5 = 2 standard deviations
z-score for 20 is (20-25)/2.5 = -2 standard deviations
this falls on the 95% (2 standard deviations)
2) z-score for 25 is (25-25)/2.5 = 0 standard deviations
z-score for 32.5 is (32.5-25)/2.5 = 3 standard deviations
this falls within the 99.7% (3 standard deviations)
Answer by mikeebsc(26)  (Show Source):
You can put this solution on YOUR website! I get a slightly different answer for #2. The math for the z-scores is correct, but the area under them is not.
For it to be 99.7, the z-scores would have to be -3 and 3, encompassing the entire area under the bell curve (using the empirical values).
If we draw out the bell curve, we see that the first point is in the middle(the given mean).
So, the actual area under these 2 points is 49.85%.
We can achieve this 2 ways:
1. Simply divide 99.7/2 or
2. take 68/2=34 (representing 1 std dev to the right of the mean), add 13.5 (which is 95-68/2: representing 2 std dev to the right of the mean), and add 2.35 ( which is 99.7-95/2 representing 3 std dev to the right of the mean.
Point out where I'm wrong if I am, but after actually drawing the bell curve, it becomes very obvious the area under the points is approximately 50%. No worries, I make mistakes all the time :).
That said, your question was helping with the formula, which the original person answering got 100% correct: Z=(value-mean)/std dev
Good luck and hope this helps,
Mike
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