Compute the Mean and Standard Deviation of a Binomial Random Variable
-A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 60 adults over 50, what is the mean and standard deviation of those that wear sunglasses
A) mean: 42; standard deviation: 3.54964787
B) mean: 42; standard deviation: 6.4807407
C) mean: 18; standard deviation: 3.54964787
D) mean: 18; standard deviation: 6.4807407

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, 60 adults) and $p$ is the probability of success (in this case, 70% or 0.7). Thus, the mean is $60 \times 0.7 = 42$. The standard deviation is given by $\sqrt{n \times p \times (1-p)}$, which calculates to $\sqrt{60 \times 0.7 \times 0.3} = 3.54964787$.