Question

5.5.17 Question Help 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 deviation. If you cannot, explain why standard found tha 45% have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them it they have used a mult past 12 months. a in in the Select the correct answer below and, if necessary, fll in the answer boxes within your choice. O A. No, because np <5 O B. No, because nq <5 O C. Yes, the mean is and the standard deviation is Round to two decimal places as needed.) ck to select and enter your answerls) and then click Check Answer

Answer 1

Solution: We are given:

$n=40$

Proportion of adults who have used multivitamin in the past 12 months is $p=0.45$

$\Rightarrow$ $q=(1-p)=1-0.45=0.55$

Therefore, $n\times p=40 \times 0.45=18$

$n\times q=40 \times 0.55=22$

Since both and are greater than 5, therefore, we can use normal distribution to approximate binomial distribution.

$Mean=n\times p=40 \times 0.45=18$

$Standard-deviation=\sqrt{n\times p \times q}=\sqrt{40 \times 0.45 \times 0.55}=3.15$

Therefore, the correct option is:

C. Yes, the mean is $18\mathbf{}$ and the standard deviation is $3.15\mathbf{}$