According to government data, the probability that an adult was never in a museum is 20%. In a randomsurvey of 70 adults, what is the mean and standard deviation of the number that were never in a museum?
A) mean: 14; standard deviation: 3.34664011
B) mean: 56 standard deviation: 3.74165739
C) mean: 56; standard deviation: 3.34664011
D) mean: 14; standard deviation: 3.74165739

Question

Quizplus · Accepted Answer

The mean is calculated as the total number of adults (70) multiplied by the probability of never being in a museum (20% or 0.2), which equals 14. The standard deviation is calculated using the formula for the standard deviation of a binomial distribution, $\sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials (70), and $p$ is the probability of success (0.2). This calculation gives $\sqrt{70 \cdot 0.2 \cdot 0.8} = 3.346640106$.

According to Government Data, the Probability That an Adult Was