A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement.

Question:

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, the $\left(\frac{\text { mean of } X}{\text { standard deviation of } X}\right)$ is equal to:-

  1. 4

  2. $\frac{4 \sqrt{3}}{3}$

  3. $4 \sqrt{3}$

  4. $3 \sqrt{2}$


Correct Option: , 3

Solution:

$p$ (probability of getting white ball) $=\frac{30}{40}$

$\mathrm{q}=\frac{1}{4}$ and $\mathrm{n}=16$

mean $=n p=16 \cdot \frac{3}{4}=12$

and standard diviation

$=\sqrt{\mathrm{npq}}=\sqrt{16 \cdot \frac{3}{4} \cdot \frac{1}{4}}=\sqrt{3}$

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