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 83​% of parents of teenagers have taken their​ teenager's cell phone or Internet privileges away as a punishment. You randomly select 19 parents of teenagers and ask them whether they have taken their​ teenager's 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 _____

B.) No because nq<5

C.) No because np<5

Answer 1

given that, 83% of parents of teenagers have taken their teenagers cell phone or internet privileges away as a punishment.

i.e. p=0.83 and given n=19 we have given binomial distribution with (n=19,p=0.83) ,q=1-p=1-0.83 =0.17

we have np= 15.77 and nq= 3.23

we know that , the binomial distribution can be approximated to normal distribution if np and nq are both at least 5.

but here nq is less than 5. hence the binomial distribution cannot be approximated to normal distribution .

correct option is:

B.) No, because nq<5