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# EX 12 - STAT 400 Examples for Spring 2011 0.1 A fair...

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STAT 400 Examples for 03/16/2010 Spring 2011 0.1. A fair 6-sided die is rolled 180 times. The sum of the outcomes is likely to be around __________, give or take __________ or so. The average of the outcomes is likely to be around __________, give or take __________ or so. μ = 6 21 6 6 5 4 3 2 1 = + + + + + = 3.5 . σ = ( ) ( ) ( ) ( ) ( ) ( ) 6 5 . 3 6 5 . 3 5 5 . 3 4 5 . 3 3 5 . 3 2 5 . 3 1 2 2 2 2 2 2 - + - + - + - + - + - = 6 5 . 17 6 25 . 6 25 . 2 25 . 0 25 . 0 25 . 2 25 . 6 = + + + + + 1.708 . E ( Sum ) = n × μ = 180 × 3.5 = 630 . SD ( Sum ) = n × σ 180 × 1.708 22.9 . The sum of the outcomes is likely to be around 630 , give or take 23 or so. E ( Average ) = μ = 3.5 . SD ( Average ) = σ n 180 708 . 1 0.1273 . The average of the outcomes is likely to be around 3.5 , give or take 0.13 or so. 0.2. A fair 6-sided die is rolled 180 times. The number of 6’s is likely to be around __________, give or take __________ or so. Let X denote the number of 6’s. Binomial distribution, n = 180 , p = 1 / 6 . E ( X ) = n × p = 180 × 1 / 6 = 30 . SD ( X ) = ( ) 1 p p n - × × = 6 5 6 1 180 × × = 5 . The number of 6’s is likely to be around 30 , give or take 5 or so.

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Case 1 . Any population n large Case 2 . Normal population Any n Case 3 . Population NOT Normal n small frownface ½ .
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