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# HW1sol - STAT 415 SOLUTIONS FOR HWK#1(by Shengzhong Su...

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STAT 415 SOLUTIONS FOR HWK #1 (by Shengzhong Su) 5.2-3. (a) , (b) , (c) 0.01 2.326 z = 0.005 2.576 z = − 0.0475 1.67 z = , (d) 0.985 1 0.985 0.015 2.17 z z z = − = − = − 5.2-4. (a) , (b) , (c) 0.10 1.282 z = 0.05 1.645 z = − 0.0485 1.66 z = − , (d) 0.9656 1 0.9656 0.0344 1.82 z z z = − = − = − 5.2-5. (a) 0.025 1.960 c z = = (b) ( ) 1 ( ) 1 [ ( ) ( )] 1 2 ( ) 0. P Z c P Z c P Z c P Z c P Z c = > = > + < − = > = 95 , so , thus ( ) 0.025 P Z c > = 0.025 1.960 c z = = (c) 0.05 1.645 c z = = (d) ( ) 1 ( ) 1 2 ( ) 0.90 P Z c P Z c P Z c = > = > = ( ) 0.05 P Z c > = , , so 0.05 1.645 c z = = Problem A. (a) 6 6 ( ) 0.025 5 5 X b P X b P = = , 0.025 6 1.960 5 b z = = , so 15.8 b = (b) (6 6 ) ( 6 ) ( 6 ) 0.975 P c X c P c X c P X c + = = = , so ( 6 ) 1 ( 6 ) 0.02 P X c P X c > = = 5 , thus ( 6 ) ( 6 ) / 2 0.0125 P X c P X c > = > = , . ( 6 ) ( 6 ) 0.0125 P X c P X c > = > + = 6 6 6 ( 6 ) 0.0125 5 5 X c P X c P + > + = > = , 0.0125 2.24 5 c z = = , . 11.20 c = 5.2-7. , so 6 X μ = and 5 X σ = . (6,25) X N : 0 6 6 8 6 (0 8) ( 1.2 0.4) (0.4) ( 1.2) 5 5 5 (0.4) [1 (1.2)]

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