Question

a recent survey found that 60% of all adults over 50 wear sunglasses for driving. in a random sample of 40 adults over 50, what is the mean and standard deviation of those that wear sunglasses? round to three decimal places

a. mean 24, standard deviation 1.549
b. mean 16, standard deviation 3.098
c. mean 24, standard deviation 3.098
d. mean 16, standard deviation 1.549

Explanation:

Step1: Calculate the mean

The formula for the mean of a binomial distribution is $\mu = np$. Here, $n = 40$ (sample size) and $p=0.6$ (probability of success).
$\mu=40\times0.6 = 24$

Step2: Calculate the standard deviation

The formula for the standard deviation of a binomial distribution is $\sigma=\sqrt{np(1 - p)}$. Substitute $n = 40$ and $p = 0.6$ into the formula.
First, calculate $np(1 - p)=40\times0.6\times(1 - 0.6)=40\times0.6\times0.4 = 9.6$
Then, $\sigma=\sqrt{9.6}\approx3.098$

Answer:

C. mean 24, standard deviation 3.098