((⊸JS⊸)/△) If a random variable X follows normal distribution with mean 30 and variance 25. What is the probalility of X is less than 28 ?


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Question Number 108334 by john santu last updated on 16/Aug/20

$\frac{⊸ J S ⊸}{△}$ $I f a r a n d o m v a r i a b l e X f o l l o w s n o r m a l$ $d i s t r i b u t i o n w i t h m e a n 30 a n d$ $v a r i a n c e 25 . W h a t i s t h e p r o b a l i l i t y$ $o f X i s l e s s t h a n 28 ?$
	Answered by bemath last updated on 17/Aug/20

	$\frac{△ B e M a t h △}{△}$ $X \sim N (30, 25)$ $P (X < 28) ?$ $z = \frac{x - μ}{σ} = \frac{28 - 30}{\sqrt{25}} = - \frac{2}{5} = - 0.4$ $P (X < 28) = P (z < - 0.4)$ $= 1 - P (z ⩽ 0.4)$ $= 1 - 0.6554$ $= 0.3446$
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