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

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$4 \sqrt{3}$

$3 \sqrt{2}$

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

answer is B.

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Detailed Solution

P (Probability of getting which ball) $= \frac{30}{40}$

$p = \frac{3}{4}, q = 1 - p = \frac{1}{4}, n = 16$

mean $(np) = 16 \times \frac{3}{4} = 12$ and

standard deviation $= \sqrt{npq}$

$= \sqrt{16 (\frac{3}{4}) (\frac{1}{4})} = \sqrt{3}$

Now $\frac{mean of X}{standard deviation of X} = \frac{12}{\sqrt{3}} = 4 \sqrt{3}$

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