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The weights of 4000 students are found to be normally distributed with mean 50 kgs & s.d. 5kgs. Find probability that a student selected at random will have weight i) $< 45$kgs. ii) between 45 & 60 kg

Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV

Marks: 6M

Year: Dec 2014

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$\mathrm{Means}\left(\mathrm{m}\right)\mathrm{=50}$, 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 $$\mathrm{z=}\frac{\mathrm{45-50}}{\mathrm{5}}\mathrm{=}-1$$ $$\mathrm{\therefore }\mathrm{p}\left(\mathrm{\times \lt45}\right)\mathrm{=p(z\lt -1)}$$

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$$\therefore p\left(z\lt-1\right)=0.5-Area\ Between\ z=0\ to\ z=-1$$

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 $$\mathrm{z=}\frac{\mathrm{45-50}}{\mathrm{5}}\mathrm{ =}2$$ $$p(45\lt\times \lt60P=p(-1\lt z \lt2)=Area\ between\ z=0\ to\ z-=1+Area\ between\ z=0\ to\ z=2$$

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$$=0.3413+0.4772$$ $$=0.8185$$ $$\therefore p\left(less\ than\ 45\ kg\right)=0.1587\&\ p\left(between\ 45\ \&\ 60\ kg\right)=0.8185$$

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