Question Number 152940 by nadovic last updated on 03/Sep/21 $$\:\mathrm{In}\:\mathrm{bottle}\:\mathrm{manufacturing}\:\mathrm{company},\:\mathrm{it} \\ $$$$\mathrm{was}\:\mathrm{observed}\:\mathrm{that}\:\mathrm{5\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bottles} \\ $$$$\mathrm{manufactured}\:\mathrm{were}\:\mathrm{defective}.\:\mathrm{In}\:\mathrm{a}\: \\ $$$$\mathrm{random}\:\mathrm{sample}\:\mathrm{of}\:\mathrm{150}\:\mathrm{bottles},\:\mathrm{find}\: \\ $$$$\mathrm{probability}\:\mathrm{that}\: \\ $$$$\:\left({a}\right)\:\mathrm{exactly}\:\mathrm{3}, \\ $$$$\:\left({b}\right)\:\mathrm{between}\:\mathrm{3}\:\mathrm{and}\:\mathrm{6}, \\ $$$$\:\left({c}\right)\:\mathrm{at}\:\mathrm{most}\:\mathrm{4}, \\…
Question Number 152937 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{4}\right).\:\mathrm{mean}\rightarrow\overset{−} {\mathrm{x}}\:=\frac{\Sigma\mathrm{x}_{\mathrm{i}} ×\mathrm{f}_{\mathrm{i}} }{\Sigma\mathrm{f}_{\mathrm{i}} } \\ $$$$\:\:\:\:\:\overset{−} {\mathrm{x}}=\frac{\mathrm{4}×\mathrm{33}+\mathrm{7}×\mathrm{38}+\mathrm{9}×\mathrm{43}+\mathrm{6}×\mathrm{48}+\mathrm{4}×\mathrm{53}}{\mathrm{30}} \\…
Question Number 152935 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{3}.\mathrm{a}\right).\:\mathrm{Q}_{\mathrm{2}} =\mathrm{L}_{\mathrm{i}} +\left(\frac{\mathrm{N}/\mathrm{2}−<\Sigma\mathrm{f}}{\Sigma\mathrm{f}_{\mathrm{i}} }\right)×\mathrm{C} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left(\mathrm{45}−\mathrm{0}.\mathrm{5}\right)+\left(\frac{\mathrm{40}/\mathrm{2}−\mathrm{16}}{\mathrm{12}}\right)×\mathrm{5} \\ $$$$\:\:\:\:\:=\mathrm{44},\mathrm{5}+\frac{\mathrm{4}×\mathrm{5}}{\mathrm{12}}=\mathrm{44},\mathrm{5}+\mathrm{1},\mathrm{67} \\…
Question Number 152903 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{1}.\mathrm{a}\right).\:\overset{−} {\mathrm{x}}\:=\:\frac{\Sigma\mathrm{f}_{\mathrm{i}} .\mathrm{x}_{\mathrm{i}} }{\Sigma\mathrm{f}_{\mathrm{i}} }\: \\ $$$$\:=\frac{\mathrm{2}×\mathrm{14},\mathrm{5}+\mathrm{9}×\mathrm{18},\mathrm{5}+\mathrm{12}×\mathrm{22},\mathrm{5}+\mathrm{9}×\mathrm{26},\mathrm{5}+\mathrm{5}×\mathrm{30},\mathrm{5}+\mathrm{3}×\mathrm{34},\mathrm{5}}{\mathrm{2}+\mathrm{9}+\mathrm{12}+\mathrm{9}+\mathrm{5}+\mathrm{3}} \\ $$$$=\frac{\mathrm{29}+\mathrm{166},\mathrm{5}+\mathrm{270}+\mathrm{238},\mathrm{5}+\mathrm{152},\mathrm{5}+\mathrm{103},\mathrm{5}}{\mathrm{40}}…
Question Number 152683 by rexford last updated on 31/Aug/21 $${The}\:{probability}\:{that}\:{athlete}\:{will}\:{win}\:{a}\:{race}\:{is}\:\frac{\mathrm{1}}{\mathrm{6}}\:{and}\:{that} \\ $$$${he}\:{will}\:{be}\:{second}\:{and}\:{third}\:{are}\:\frac{\mathrm{1}}{\mathrm{4}}\:{and}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${respectively}.{what}\:{is}\:{the}\:{probability}\:{that}\:{he}\:{will}\:{not}\:{be}\:{first} \\ $$$${in}\:{the}\:{first}\:{three}\:{place}! \\ $$$${Please},{help}\:{me}\:{out} \\ $$ Answered by Olaf_Thorendsen last updated…
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Question Number 86668 by jagoll last updated on 30/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{P}\left(\mid\mathrm{x}\mid\:>\:\mathrm{1}\:\right)\:\mathrm{if}\:\mathrm{x}\:\mathrm{has}\:\mathrm{a}\:\mathrm{PDF}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\begin{cases}{\frac{\mathrm{1}}{\mathrm{4}}\:,\:\:−\mathrm{2}<\mathrm{x}<\mathrm{2}}\\{\mathrm{0}\:,\:\mathrm{elsewhere}}\end{cases} \\ $$ Commented by john santu last updated on 30/Mar/20 $$\Rightarrow\mathrm{P}\left(\mathrm{x}<−\mathrm{1}\:\cup\:\mathrm{x}>\mathrm{1}\right) \\ $$$$=\:\int_{−\mathrm{2}}…
Question Number 151602 by DELETED last updated on 22/Aug/21 Answered by DELETED last updated on 22/Aug/21 $$\left.\mathrm{1}.\mathrm{g}\right).\:\mathrm{Letak}\:\mathrm{persentil}\:\mathrm{ke}−\mathrm{65} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{P}_{\mathrm{i}} =\frac{\mathrm{i}\left(\mathrm{N}+\mathrm{1}\right)}{\mathrm{100}}\:\rightarrow\mathrm{P}_{\mathrm{65}} \:=\frac{\mathrm{65}\left(\mathrm{25}+\mathrm{1}\right)}{\mathrm{100}} \\ $$$$\:\:\:\:=\frac{\mathrm{65}×\mathrm{26}}{\mathrm{100}}=\mathrm{16},\mathrm{9} \\ $$$$\:\:\:\:\mathrm{Nilai}\:\mathrm{persentil}\:\mathrm{ke}\:\mathrm{65}=\mathrm{x}_{\mathrm{16}}…
Question Number 151454 by gsk2684 last updated on 21/Aug/21 $${when}\:{a}\:{die}\:{is}\:{rolled}\:\mathrm{42}\:{times}\:{it}\:{is}\:{so} \\ $$$${happened}\:{that}\:{a}\:{face}\:{having}\:{the}\:{digit}\:{i} \\ $$$${times}\:{occured}\:\mathrm{2}{i}\:{times}.\:{then}\:{find}\:{the} \\ $$$${mean}\:{deviation}\:{from}\:{the}\:{mean}\:{of}\:{this} \\ $$$${discrete}\:{frequency}\:{distribution}. \\ $$$${ans}\:{is}\:\frac{\mathrm{80}}{\mathrm{63}} \\ $$$${sol}\:{pls} \\ $$ Commented…
Question Number 85859 by jagoll last updated on 25/Mar/20 $$\:\mathrm{Is}\:\mathrm{the}\:\mathrm{Var}\left(\mathrm{aX}+\mathrm{b}\right)\:=\:\mathrm{a}^{\mathrm{2}} \:\mathrm{Var}\left(\mathrm{X}\right)\:+\:\mathrm{b}? \\ $$ Answered by Joel578 last updated on 25/Mar/20 $${nope} \\ $$$$\mathrm{Assume}\:{a}\:\mathrm{and}\:{b}\:\mathrm{is}\:\mathrm{constant},\:\mathrm{then} \\ $$$$\mathrm{var}\left({b}\right)\:=\:{E}\left[{b}^{\mathrm{2}}…