Question

(About Moivre Laplace theorem in probability theory). There are 5 boxes – one of them is red, the rest are green. By chance, every one of 2500 balls is thrown into one of the boxes. Find out the probability that the number of the balls in the red box (I) will not be greater than 523; (II) will not be less than 490; (III) will not be greater than 523 and will not be less than 490.

Answer 1

n=	2500	p=	0.2000
here mean of distribution=μ=np=		500
and standard deviation σ=sqrt(np(1-p))=		20.0000
for normal distribution z score =(X-μ)/σx

i)

  number of the balls in the red box (I) will not be greater than 523:

probability =

P(X<523)

=

P(Z<1.15)=

0.8749

ii)

probability =

P(X>490)

=

P(Z>-0.5)=

1-P(Z<-0.5)=

1-0.3085=

0.6915

iii)

probability =

P(490<X<523)

=

P(-0.5<Z<1.15)=

0.8749-0.3085=

0.5664