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Category: Probability and Statistics

The-mean-weights-of-three-groups-of-students-consisting-of-16-18-and-20-students-are-40-5kg-42-50kg-and-45-00kg-respectively-What-is-the-mean-weight-of-all-the-students-

Question Number 25549 by pieroo last updated on 11/Dec/17 $$\mathrm{The}\:\mathrm{mean}\:\mathrm{weights}\:\mathrm{of}\:\mathrm{three}\:\mathrm{groups}\:\mathrm{of}\:\mathrm{students} \\ $$$$\mathrm{consisting}\:\mathrm{of}\:\mathrm{16},\:\mathrm{18}\:\mathrm{and}\:\mathrm{20}\:\mathrm{students}\:\mathrm{are}\:\mathrm{40}.\mathrm{5kg},\:\mathrm{42}.\mathrm{50kg} \\ $$$$\mathrm{and}\:\mathrm{45}.\mathrm{00kg}\:\mathrm{respectively}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{weight} \\ $$$$\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{students}? \\ $$ Answered by Rasheed.Sindhi last updated on 11/Dec/17…

Question-90258

Question Number 90258 by jagoll last updated on 22/Apr/20 Commented by john santu last updated on 22/Apr/20 $$\left({a}\right){P}\left({X}\leqslant\mathrm{3}\right)\:=\:\underset{{k}\:=\:\mathrm{0}} {\overset{\mathrm{3}} {\sum}}{C}_{{k}} ^{\mathrm{25}} \left(\mathrm{0}.\mathrm{05}\right)^{{k}} \:\left(\mathrm{0}.\mathrm{95}\right)^{\mathrm{3}−{k}} \\ $$$$\left({b}\right){P}\left({X}\geqslant\mathrm{4}\right)\:=\:\mathrm{1}−\underset{{k}\:=\:\mathrm{0}}…

A-bag-contains-5-balls-2-green-and-3red-They-are-selected-without-replacement-till-the-remaining-balls-in-the-bag-are-of-same-colours-Let-the-random-variable-X-be-the-number-of-selections-possible-1

Question Number 90196 by Ar Brandon last updated on 21/Apr/20 $$\mathrm{A}\:\mathrm{bag}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{balls},\:\mathrm{2}\:\mathrm{green}\:\mathrm{and}\:\mathrm{3red} \\ $$$$\mathrm{They}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{till} \\ $$$$\mathrm{the}\:\mathrm{remaining}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{are}\:\mathrm{of}\:\mathrm{same}\:\mathrm{colours}. \\ $$$$\mathrm{Let}\:\mathrm{the}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{X}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{selections}\:\mathrm{possible} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{X} \\ $$$$\left.\mathrm{2}\right)\mathrm{Determine}\:\mathrm{the}\:\mathrm{it}'\mathrm{s}\:\mathrm{expectation},\:\mathrm{its}\:\mathrm{variance} \\ $$$$\mathrm{and}\:\mathrm{its}\:\mathrm{standard}\:\mathrm{deviation}.…

I-hold-my-hand-behind-my-back-and-secretly-hold-up-n-fingers-0-n-5-I-then-as-you-am-I-holding-up-k-fingers-Where-k-is-also-a-random-number-0-k-5-You-randomly-guess-Yes-or-No-What-is-the-pr

Question Number 24490 by FilupES last updated on 19/Nov/17 $$\mathrm{I}\:\mathrm{hold}\:\mathrm{my}\:\mathrm{hand}\:\mathrm{behind}\:\mathrm{my}\:\mathrm{back},\:\mathrm{and}\:\mathrm{secretly} \\ $$$$\mathrm{hold}\:\mathrm{up}\:{n}\:\mathrm{fingers}\:\left(\mathrm{0}\leqslant{n}\leqslant\mathrm{5}\right). \\ $$$$\: \\ $$$$\mathrm{I}\:\mathrm{then}\:\mathrm{as}\:\mathrm{you},\:\mathrm{am}\:\mathrm{I}\:\mathrm{holding}\:\mathrm{up}\:{k}\:\mathrm{fingers}? \\ $$$$\mathrm{Where}\:{k}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{random}\:\mathrm{number}\:\mathrm{0}\leqslant{k}\leqslant\mathrm{5}. \\ $$$$\: \\ $$$$\mathrm{You}\:\mathrm{randomly}\:\mathrm{guess}\:\mathrm{Yes}\:\mathrm{or}\:\mathrm{No}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{you}\:\mathrm{guess}\:\mathrm{correctly}? \\…

In-a-classroom-when-the-students-sit-2-per-bench-11-students-are-left-with-no-sits-And-when-they-sit-3-per-bench-7-benches-are-left-empty-Determine-the-number-of-students-in-this-classroom-

Question Number 89898 by Ar Brandon last updated on 19/Apr/20 $${In}\:{a}\:{classroom}\:{when}\:{the}\:{students}\:{sit} \\ $$$$\mathrm{2}\:{per}\:{bench},\:\mathrm{11}\:{students}\:{are}\:{left}\:{with} \\ $$$${no}\:{sits}.\:{And}\:{when}\:{they}\:{sit}\:\mathrm{3}\:{per}\:{bench} \\ $$$$\mathrm{7}\:{benches}\:{are}\:{left}\:{empty}.\:{Determine}\:{the}\:{number} \\ $$$${of}\:{students}\:{in}\:{this}\:{classroom}. \\ $$ Commented by MJS last…

P-X-299-318-standard-deviation-42-P-z-299-318-42-P-z-0-45-Is-it-P-z-0-45-P-0-45-lt-z-lt-0-44-If-not-how-to-find-P-z-0-45-

Question Number 23781 by alibhar last updated on 06/Nov/17 $${P}\left({X}=\mathrm{299}\right),\:\mu=\mathrm{318},\:{standard}\:{deviation}=\mathrm{42} \\ $$$${P}\left({z}=\frac{\mathrm{299}−\mathrm{318}}{\mathrm{42}}\right) \\ $$$${P}\left({z}=−\mathrm{0}.\mathrm{45}\right) \\ $$$$ \\ $$$${Is}\:{it}\:{P}\left({z}=−\mathrm{0}.\mathrm{45}\right)={P}\left(−\mathrm{0}.\mathrm{45}<{z}<−\mathrm{0}.\mathrm{44}\right)? \\ $$$$ \\ $$$${If}\:{not},\:{how}\:{to}\:{find}\:{P}\left({z}=−\mathrm{0}.\mathrm{45}\right)? \\ $$ Terms…