Compute the Mean and Standard Deviation of a Binomial Random Variable
-According to government data, the probability that an adult was never in a museum is 13%. In a random survey of 20 adults, what is the mean and standard deviation of the number that were never in a museum
A) mean: 2.6; standard deviation: 1.50399468
B) mean: 17.4 standard deviation: 1.61245155
C) mean: 17.4; standard deviation: 1.50399468
D) mean: 2.6; standard deviation: 1.61245155

Question

Quizplus · Accepted Answer

The mean of a binomial distribution is given by $n \times p$, where $n$ is the number of trials and $p$ is the probability of success. Here, $n = 20$ and $p = 0.13$, so the mean is $20 \times 0.13 = 2.6$. The standard deviation is given by $\sqrt{n \times p \times (1-p)}$, which calculates to $\sqrt{20 \times 0.13 \times (1-0.13)} = 1.50399468$.