Compute the Mean and Standard Deviation of a Binomial Random Variable
-The probability that a football game will go into overtime is 14%. In 140 randomly selected football games, what is the mean and the standard deviation of the number that went into overtime
A) mean: 19.6; standard deviation: 4.10560592
B) mean: 19.6; standard deviation: 4.42718872
C) mean: 18.2; standard deviation: 4.10560592
D) mean: 18.2; standard deviation: 4.42718872

Question

Quizplus · Accepted Answer

The mean of a binomial distribution is given by $ \mu = np $, where $ n $ is the number of trials and $ p $ is the probability of success on each trial. Here, $ n = 140 $ and $ p = 0.14 $, so $ \mu = 140 \times 0.14 = 19.6 $. The standard deviation is given by $ \sigma = \sqrt{np(1-p)} $, so $ \sigma = \sqrt{140 \times 0.14 \times (1 - 0.14)} = \sqrt{19.6 \times 0.86} \approx 4.10560592 $.