written 7.7 years ago by | modified 2.1 years ago by |
Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV
Marks: 6M
Year: Dec 2014
written 7.7 years ago by | modified 2.1 years ago by |
Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV
Marks: 6M
Year: Dec 2014
written 7.7 years ago by | • modified 7.7 years ago |
$\mathrm{Means}\left(\mathrm{m}\right)\mathrm{=50}$, Standard deviation r=25 Let x be weight of a student 1) P(less than 45 kg) $\mathrm{=p(\times <45)}$In terms of z using S.N.V.When x=45 $$\mathrm{z=}\frac{\mathrm{45-50}}{\mathrm{5}}\mathrm{=}-1$$ $$\mathrm{\therefore }\mathrm{p}\left(\mathrm{\times \lt45}\right)\mathrm{=p(z\lt -1)}$$
$$\therefore p\left(z\lt-1\right)=0.5-Area\ Between\ z=0\ to\ z=-1$$
Note :- Total area is 0.5
=0.5-03413
=0.1587
2) P(between 45 and 60) $=P(45\lt\times \lt60)$
In terms of z using S.N.V
When x=45 $$\mathrm{z=}\frac{\mathrm{45-50}}{\mathrm{5}}\mathrm{ =}-1$$
When x=60 $$\mathrm{z=}\frac{\mathrm{45-50}}{\mathrm{5}}\mathrm{ =}2$$ $$p(45\lt\times \lt60P=p(-1\lt z \lt2)=Area\ between\ z=0\ to\ z-=1+Area\ between\ z=0\ to\ z=2$$
$$=0.3413+0.4772$$ $$=0.8185$$ $$\therefore p\left(less\ than\ 45\ kg\right)=0.1587\&\ p\left(between\ 45\ \&\ 60\ kg\right)=0.8185$$