Compute the Mean and Standard Deviation of a Binomial Random Variable
-The probability that an individual has 20-20 vision is 0.17. In a class of 80 students, what is the mean and standard deviation of the number with 20-20 vision in the class
A) mean: 13.6; standard deviation: 3.3597619
B) mean: 80; standard deviation: 3.3597619
C) mean: 13.6; standard deviation: 3.68781778
D) mean: 80; standard deviation: 3.68781778

Question

Quizplus · Accepted Answer

The mean of a binomial distribution is given by $n \times p$, where $n$ is the number of trials (in this case, 80 students) and $p$ is the probability of success (in this case, 0.17 for having 20-20 vision). Thus, the mean is $80 \times 0.17 = 13.6$. The standard deviation is given by $\sqrt{n \times p \times (1-p)}$, which calculates to $\sqrt{80 \times 0.17 \times (1-0.17)} = 3.3597619$.