what is the mean of X? What is the standard deviation of X?

Question

The probability that any given tennis set will go to a tiebreaker is 13%. If I randomly select 260 tennis sets, with the random variable X being the number of tiebreakers, what is the mean of X? What is the standard deviation of X?

Answer 1

There are only two outcomes: the set result is a tie-break or it isn't. If p=probability of a tie-break=0.13, then q=1-p=0.87, the probability of no tie-break.

The mean is np where n=260 is the number of sets, so the mean is 0.13×260=33.8.

The variance is npq=260×0.13×0.87=29.406, and the standard deviation is the square root of this=5.42 approx.