A recent survey found that 69% of all adults over 50 wear sunglasses for driving. In a random sample of 20adults over 50, what is the mean and standard deviation of those that wear sunglasses?
A) mean: 13.8; standard deviation: 2.06833266
B) mean: 13.8; standard deviation: 3.71483512
C) mean: 6.2; standard deviation: 2.06833266
D) mean: 6.2; standard deviation: 3.71483512

Question

Quizplus · Accepted Answer

The mean of those that wear sunglasses is found by multiplying the probability by the sample size: $0.69 \times 20 = 13.8$. 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 sample size, $p$ is the probability of success (wearing sunglasses), and $1-p$ is the probability of failure. Substituting the given values: $\sqrt{20 \times 0.69 \times (1-0.69)} = 2.06833266$.

A Recent Survey Found That 69% of All Adults Over