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  • Solve this problem - A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag - Statistics and Probability - JEE Main

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 (\frac{mean \: of\: X}{standard \: deviation\: of\: X})  is equal to:

  • Option 1)

     

    \frac{4\sqrt3}{3}

  • Option 2)

     

    4

  • Option 3)

     

    3\sqrt2

  • Option 4)

     

    4\sqrt3

Answers (1)

best_answer

 

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by 

\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}

in case of discrete data.

Standard Deviation -

In case of discrete frequency distribution 

\sigma = \sqrt{\frac{\sum f_{i}x_{i}^{2}}{\sum f_{i}}-\left ( \frac{\sum f_{i}x_{i}}{\sum f_{i}} \right )^{2}}

 

P(white ball) = \frac{30}{40}=\frac{3}{4}

q=\frac{1}{4}         and    n =  16

mean (X) = np =16\times \frac{3}{4}  

                        = 12

Standard deviation (X) = \sqrt{npq}=\sqrt3

Ans. \frac{12}{\sqrt3}= 4\sqrt3


 


Option 1)

 

\frac{4\sqrt3}{3}

Option 2)

 

4

Option 3)

 

3\sqrt2

Option 4)

 

4\sqrt3
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