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# HW2_sol - 1 74 X i ~ N(100,102 n = 25 X = 100 X = n = 10 25...

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1. 7 4. 25 ) 10 , 100 ( ~ 2 = n N X i 2 25 10 100 = = = = n X X σ μ 8054 . 0 0359 . 0 8413 . 0 ) 8 . 1 ( ) 1 ( ) 1 8 . 1 ( ) 102 4 . 96 ( )] 2 100 ( )) 2 ( 8 . 1 100 [( 2 100 102 / 2 100 4 . 96 = = = = = = + Z P Z P Z P P X P X P n X 2. 7 11. n = 36 3 2 12 8 12 1 ) 1 1 3 ( 12 1 ) 1 ( 2 2 ) 1 3 ( 2 2 2 = = + = + = = + = + = a b b a X X 6 3 / 2 36 3 / 2 , 2 = = = X X n X z / = Using the central limit theorem: 2312 . 0 7688 . 0 1 ) 7348 . 0 ( ) 6742 . 3 ( ) 6742 . 3 7348 . 0 ( ) 5 . 2 1 . 2 ( 6 3 / 2 6 3 / 2 2 5 . 2 2 1 . 2 = = < < = < < = < < = < < Z P Z P Z P Z P X P

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3. 7 17. a) Note that ‘SE Mean’ means standard error of the mean. √ே SE Mean ՜ ଵ଴.ଶହ √ே ൌ2 .05՜ܰൌ25 Mean ଷ଻଺ଵ.଻଴ ଶହ ൌ 150.468 Variance ൌܵ ൌ 10.25 ൌ105 .0625 Variance = Sum of Squares ௡ିଵ ՜ 105.0625 ൌ ௌௌ ଶହିଵ ՜ ܵܵ ൌ 2521.5 b) Estimate of mean of population = sample mean = 150.468 4. 7 20. E () μ = = = = = = n n X E n n X E X n i i n i i 2 2 1 2 1 2 2 1 2 1 1 E = = =
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HW2_sol - 1 74 X i ~ N(100,102 n = 25 X = 100 X = n = 10 25...

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