Consider the following binomial experiment: A study in a certain community showed that 8% of the people suffer from insomnia. If there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia?

Answer: 27.67Step-by-step explanation:We know that the standard deviation for binomial distribution having parameter n (number of trails) and p (probability of getting succes in each trials) is [tex]\sigma=\sqrt{np(1-p)}[/tex]Given : The proportion of of the people suffer from insomnia. = 0.08The number of people in community = 10,400 Then the standard deviation of  the number of people who suffer from insomnia will be :-[tex]\sigma=\sqrt{10400(0.08)(0.92)}=27.6665863453\approx27.67[/tex]Hence, the standard deviation of the number of people who suffer from insomnia = 27.67