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A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $$\left( {{{mean\,\,of\,X} \over {s\tan dard\,\,deviation\,\,of\,X}}} \right)$$ is equal to :

JEE · Math · previous-year question

  1. A.4
  2. B.$$3\sqrt 2 $$
  3. C.$${{4\sqrt 3 } \over 3}$$
  4. D.$$4\sqrt 3 $$correct

Answer

D. $$4\sqrt 3 $$

Explanation

p (probability of getting white ball) = $${{30} \over {40}}$$ q = $${1 \over 4}$$ and n = 16 mean = np = 16.$${3 \over 4}$$ = 12 and standard diviation = $$\sqrt {npq} $$ = $$\sqrt {16.{3 \over 4}.{1 \over 4}} = \sqrt 3 $$ $$ \because $$ $$mean \over standard\,deviation$$ = $$12\over{\sqrt3}$$ = $$4{\sqrt3}$$

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