The probability that a tennis set will go to a tiebreaker is 16%. In 220 randomly selected tennis sets, what is the mean and the standard deviation of the number of tiebreakers?
A)mean: 35.2; standard deviation: 5.44
B)mean: 35.2; standard deviation: 5.93
C)mean: 33; standard deviation: 5.44
D)mean: 33; standard deviation: 5.93

Question

Quizplus · Accepted Answer

The mean of the number of tiebreakers is found by multiplying the probability of a tiebreaker by the number of sets: $220 \times 0.16 = 35.2$. The standard deviation is calculated using the formula for the standard deviation of a binomial distribution, $\sqrt{n \times p \times (1-p)}$, where $n$ is the number of trials and $p$ is the probability of success: $\sqrt{220 \times 0.16 \times (1-0.16)} = \sqrt{35.2 \times 0.84} \approx 5.44$.

The Probability That a Tennis Set Will Go to a Tiebreaker