A bag contans 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 m e a n o f X s t a n d a r d    d e v i a t i o n o f   X is equal to

Step-by-step solution

The total number of balls is 30 + 10 = 40 . The probability of drawing a white ball in a single trial is p = 30 40 = 3 4 . The probability of drawing a red ball is q = 1 - p = 1 - 3 4 = 1 4 . The number of trials is n = 16 . Since the balls are drawn with replacement, the random variable X follows a binomial distribution B(n, p) = B(16, 3 4 ) . The mean of X is given by E(X) = np = 16 3 4 = 12 . The variance of X is given by Var(X) = npq = 16 3 4 1 4 = 3 . The standard deviation of X is = Var(X) = 3 . The ratio of