Bell Curve details
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![Page 1: Bell Curve details](https://reader035.fdocuments.in/reader035/viewer/2022081816/55cf9970550346d0339d67e8/html5/thumbnails/1.jpg)
68% Area
68% of the area under the bell curve is within ONE standard deviation of the mean.
68% Area
![Page 2: Bell Curve details](https://reader035.fdocuments.in/reader035/viewer/2022081816/55cf9970550346d0339d67e8/html5/thumbnails/2.jpg)
95% Area
95% of the area under the bell curve is within TWO standard deviations of the mean.
95% Area
![Page 3: Bell Curve details](https://reader035.fdocuments.in/reader035/viewer/2022081816/55cf9970550346d0339d67e8/html5/thumbnails/3.jpg)
50% areaThe bell curve is symmetric.
This means 50% of the area is to the right of the mean, 34% between m and +m s, and 47.5% between m and -2m s.
68/2 = 34% area
95/2 = 47.5% area
![Page 4: Bell Curve details](https://reader035.fdocuments.in/reader035/viewer/2022081816/55cf9970550346d0339d67e8/html5/thumbnails/4.jpg)
.135 .135
.34 .34
.025 .025
We could separate the bell curve into six “chunks”, with areas shown below.
Again, the area within ONE s.d. of the mean is .34 + .34 = .68
Area within TWO s.d.’s of the mean is .135+.34+.34+.135 = .95
![Page 5: Bell Curve details](https://reader035.fdocuments.in/reader035/viewer/2022081816/55cf9970550346d0339d67e8/html5/thumbnails/5.jpg)
Now we can find any normal probability involving the mean plus or minus one or two standard deviations.
Example: Suppose that
X ~ N(6,9)
What is P(3<X<12)?
6 9 1230
m = 6s2 = 9 → s = 3
Here is the picture that should pop up in your head:
The probability of being between one s.d. below the mean and two s.d.’s above is: .34 + .34 + .135
= .815