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There are 30 white balls and 10 red balls in bag. 16 balls are drawn with replacement from the bag. If `X` be the number of white balls drawn then the value of `(mean(X))/(standard deviation(X))` is equal to (A) `4sqrt3` (B) `2sqrt3` (C) `3sqrt3` (D) `3sqrt2`A. `(4sqrt(3))/(3)`B. 4C. `3sqrt(2)`D. `4 sqrt(3)` |
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Answer» Correct Answer - D Number of white balls `=30` and number of red balls `=10` Let p = probability of success in a trial = probability of getting a white ball in a trial `=(30)/(40)=(3)/(4).` and q = probability of failure in a trial ` =1-p=1-(3)/(4)=(1)/(4)` Here,n = number of trials = 16. Clearly, X follows binomial distribution with parameter `n= 16 and p =(3)/(4).` `therefore " Mean of " X=np, =16.(3)/(4)=12` and variance of `X=npq=16.(3)/(4).(1)/(4)=3` Now, `("mean of X")/("standard deviation of X")=(12)/(sqrt(3))=4 sqrt(3) " " [ because SD=sqrt("variance")]` |
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