A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.
A survey of adults found that $59 \%$ have used a multivitamin in the past 12 months. You randomly select 60 adults and ask them if they have used a multivitamin in the past 12 months.
Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
A. No, because $n p< 5$.
B. No, because $\mathrm{nq}< 5$.
C. Yes, the mean is $\square$ and the standard deviation is (Round to two decimal places as needed)

Step 1 ：We are given a binomial experiment where n=60 (the number of adults selected) and p=0.59 (the probability that an adult has used a multivitamin in the past 12 months).

Step 2 ：We need to check if the binomial distribution can be approximated by a normal distribution. This is possible if both np and nq are greater than 5, where q is the probability of failure and is equal to 1-p.

Step 3 ：First, calculate q as 1-p, which gives q = 1 - 0.59 = 0.41.

Step 4 ：Next, calculate np and nq. np = 60 * 0.59 = 35.4 and nq = 60 * 0.41 = 24.6.

Step 5 ：Since both np and nq are greater than 5, we can use the normal distribution to approximate the binomial distribution.

Step 6 ：The mean of a binomial distribution is np, so the mean is 35.4.

Step 7 ：The standard deviation of a binomial distribution is \(\sqrt{npq}\). Calculate the standard deviation as \(\sqrt{60 * 0.59 * 0.41} \approx 3.81\) (rounded to two decimal places).

Step 8 ：Final Answer: Yes, the mean is \(\boxed{35.4}\) and the standard deviation is \(\boxed{3.81}\) (Round to two decimal places as needed).