Previous in Probability and Statistics Next in Probability and Statistics
Question Number 108334 by john santu last updated on 16/Aug/20
$$\:\:\:\frac{\multimap{JS}\multimap}{\bigtriangleup} \\ $$$${If}\:{a}\:{random}\:{variable}\:{X}\:{follows}\:{normal} \\ $$$${distribution}\:{with}\:{mean}\:\mathrm{30}\:{and}\: \\ $$$${variance}\:\mathrm{25}.\:{What}\:{is}\:{the}\:{probalility} \\ $$$${of}\:{X}\:{is}\:{less}\:{than}\:\mathrm{28}\:? \\ $$
Answered by bemath last updated on 17/Aug/20
$$\:\:\:\:\:\frac{\bigtriangleup\mathcal{B}{e}\mathcal{M}{ath}\bigtriangleup}{\bigtriangleup} \\ $$$${X}\:\sim\:{N}\left(\mathrm{30},\:\mathrm{25}\right) \\ $$$${P}\left({X}<\:\mathrm{28}\:\right)\:? \\ $$$${z}\:=\:\frac{{x}−\mu}{\sigma}\:=\:\frac{\mathrm{28}−\mathrm{30}}{\:\sqrt{\mathrm{25}}}\:=\:−\frac{\mathrm{2}}{\mathrm{5}}=−\mathrm{0}.\mathrm{4} \\ $$$${P}\left({X}<\mathrm{28}\right)\:=\:{P}\left({z}<−\mathrm{0}.\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{1}−{P}\left({z}\:\leqslant\mathrm{0}.\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{1}−\mathrm{0}.\mathrm{6554} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{0}.\mathrm{3446} \\ $$