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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 mean of X standard deviation of X is equal to:

3√2

4

4√33

4√3

Solution:

p(probability of getting white ball)=30/40 = 3/4
q(probability of getting red ball)=10/40 = 1/4
n=16
mean of X=np=16*(3/4)=12
variance of X=npq=16*(3/4)*(1/4)=3
standard deviation of X=√variance=√3
Therefore, mean of X = 12 and standard deviation of X = √3