a : 200 ⋅ 0.674 = 134.8 T h e n u m b e r w i l l b e a r o u n d 135 b : P ( p ^ ⩾ 147 200 ) = P ( n p ^ − p p ( 1 − p ) ⩾ n 147 200 − p p ( 1 − p ) ) = = P ( Z ⩾ 200 147 200 − 0.674 0.674 ( 1 − 0.674 ) ) = P ( Z ⩾ 1.8404 ) = = Φ ( − 1.8404 ) = 0.033 T h e p r o b a b i l i t y t o o b t a i n 147 o r m o r e m u r d e r s b y f i r e a r m o f 200 i s l e s s t h a n 4 % . T h u s t h i s i s u n u s u a l . a:\\200\cdot 0.674=134.8\\The\,\,number\,\,will\,\,be\,\,around\,\,135\\b:\\P\left( \hat{p}\geqslant \frac{147}{200} \right) =P\left( \sqrt{n}\frac{\hat{p}-p}{\sqrt{p\left( 1-p \right)}}\geqslant \sqrt{n}\frac{\frac{147}{200}-p}{\sqrt{p\left( 1-p \right)}} \right) =\\=P\left( Z\geqslant \sqrt{200}\frac{\frac{147}{200}-0.674}{\sqrt{0.674\left( 1-0.674 \right)}} \right) =P\left( Z\geqslant 1.8404 \right) =\\=\varPhi \left( -1.8404 \right) =0.033\\The\,\,probability\,\,to\,\,obtain\,\,147 or\,\,more\,\,murders\,\,by\,\,firearm\,\,of\,\,200 is\,\,less\,\,than\,\,4\%. \\Thus\,\,this\,\,is\,\,unusual. a : 200 ⋅ 0.674 = 134.8 T h e n u mb er w i ll b e a ro u n d 135 b : P ( p ^ ⩾ 200 147 ) = P ( n p ( 1 − p ) p ^ − p ⩾ n p ( 1 − p ) 200 147 − p ) = = P ( Z ⩾ 200 0.674 ( 1 − 0.674 ) 200 147 − 0.674 ) = P ( Z ⩾ 1.8404 ) = = Φ ( − 1.8404 ) = 0.033 T h e p ro babi l i t y t o o b t ain 147 or m ore m u r d ers b y f i re a r m o f 200 i s l ess t han 4%. T h u s t hi s i s u n u s u a l .
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