Question

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 found that 84% of parents of teenagers have taken their teenagers cell phone or internet privileges away as a punishment. you randomly select 12 parents of teenagers and ask them whether they have taken their teenagers cell phone or internet privileges away as a punishment. select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. a. yes, the mean is and the standard deviation is (round to two decimal places as needed.) b. no, because np < 5. c. no, because nq < 5.

Explanation:

Step1: Check the conditions for normal approximation

For a binomial distribution \(X\sim B(n,p)\) to be approximated by a normal distribution \(N(np, npq)\), we need \(np\geq5\) and \(nq\geq5\), where \(q = 1 - p\).
Given \(n = 12\), \(p=0.84\), then \(q=1 - 0.84 = 0.16\).
Calculate \(np\):
\(np=12\times0.84 = 10.08\)
Calculate \(nq\):
\(nq=12\times0.16 = 1.92\)
Since \(nq = 1.92<5\), we cannot use the normal distribution to approximate the binomial distribution.

Answer:

C. No, because \(nq<5\).