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Warm-up March 18, 2013

Warm-up March 18, 2013. 68% of the area under the bell curve is within ONE standard deviation of the mean. 68% Area. 68% Area. 95% of the area under the bell curve is within TWO standard deviations of the mean. 95% Area. 95% Area. The bell curve is symmetric.

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Warm-up March 18, 2013

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  1. Warm-up March 18, 2013

  2. 68% of the area under the bell curve is within ONE standard deviation of the mean. 68% Area 68% Area

  3. 95% of the area under the bell curve is within TWO standard deviations of the mean. 95% Area 95% Area

  4. The 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 m-2s. 50% area 68/2 = 34% area 95/2 = 47.5% area

  5. 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 .34 .34 .025 .025 .135 .135

  6. 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)? m = 6 s2 = 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 0 3 6 9 12

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