DS212_HW5_Solutions

DS212_HW5_Solutions - DS 212 Business Statistics Soorapanth...

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DS 212 Business Statistics Soorapanth Homework #5 Solutions 5.1 x P ( x ) x · P ( x ) ( x - µ ) 2 ( x - µ ) 2 · P ( x ) 1 .238 .238 2.775556 0.6605823 2 .290 .580 0.443556 0.1286312 3 .177 .531 0.111556 0.0197454 4 .158 .632 1.779556 0.2811700 5 .137 .685 5.447556 0.7463152 µ = [ x · P ( x )] = 2.666 σ 2 = [( x - µ ) 2 · P ( x )] = 1.836444 σ = 836444 . 1 = 1.355155 5.2 x P ( x ) x · P ( x ) ( x - µ ) 2 ( x - µ ) 2 · P ( x ) 0 .103 .000 7.573504 0.780071 1 .118 .118 3.069504 0.362201 2 .246 .492 0.565504 0.139114 3 .229 .687 0.061504 0.014084 4 .138 .552 1.557504 0.214936 5 .094 .470 5.053504 0.475029 6 .071 .426 10.549500 0.749015 7 .001 .007 18.045500 0.018046 µ = [ x · P ( x )] = 2.752 σ 2 = [( x - µ ) 2 · P ( x )] = 2.752496 σ = 752496 . 2 = 1.6591 5.3 x P ( x ) x · P ( x ) ( x - µ ) 2 ( x - µ ) 2 · P ( x ) 0 .461 .000 0.913936 0.421324 1 .285 .285 0.001936 0.000552 2 .129 .258 1.089936 0.140602 3 .087 .261 4.177936 0.363480 4 .038 .152 9.265936 0.352106 E ( x ) = µ = [ x · P ( x )]= 0.956 σ 2 = [( x - µ ) 2 · P ( x )] = 1.278064 σ = 278064 . 1 = 1.1305 1
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DS 212 Business Statistics Soorapanth 5.5 a) n = 4 p = .10 q = .90 P ( x =3) = 4 C 3 (.10) 3 (.90) 1 = 4(.001)(.90) = .0036 b) n = 7 p = .80 q = .20 P ( x =4) = 7 C 4 (.80) 4 (.20) 3 = 35(.4096)(.008) = .1147 c) n = 10 p = .60 q = .40 P ( x > 7) = P ( x =7) + P ( x =8) + P ( x =9) + P ( x =10) = 10 C 7 (.60) 7 (.40) 3 + 10 C 8 (.60) 8 (.40) 2 + 10 C 9 (.60) 9 (.40) 1 + 10 C 10 (.60) 10 (.40) 0 = 120(.0280)(.064) + 45(.0168)(.16) + 10(.0101)(.40) + 1(.0060)(1)= .2150 + .1209 + .0403 + .0060 = .3822 d) n = 12 p = .45 q = .55 P (5 < x < 7) = P ( x =5) + P ( x =6) + P ( x =7) = 12 C 5 (.45) 5 (.55) 7 + 12 C 6 (.45) 6 (.55) 6 + 12 C 7 (.45) 7 (.55) 5 = 792(.0185)(.0152) + 924(.0083)(.0277) + 792(.0037)(.0503) = .2225 + .2124 + .1489 = .5838 5.6 By Table A.2: a) n = 20 p = .50 P ( x =12) = .120 b) n = 20 p = .30 P ( x > 8) = P (x=9) + P ( x =10) + P ( x =11) + ...+ P ( x =20) = .065 + .031 + .012 + .004 + .001 + .000 = .113 2
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DS 212 Business Statistics Soorapanth
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