The U.S. Centers for Disease Control announced that skin allergies have risen among U.S. children to 12.5%.22 Serious allergies can affect a child’s education, sleep, and ordinary daily activities....

The U.S. Centers for Disease Control announced that skin allergies have risen among U.S. children to 12.5%.22 Serious allergies can affect a child’s education, sleep, and ordinary daily activities. Suppose 320 U.S. children are randomly selected and tested for skin allergies.

 a. Find the probability that the sample proportion of children with skin allergies is less than 0.10.

b. Find the probability that the sample proportion of children with skin allergies is between 0.08 and 0.16.

c. Suppose 150 U.S. children aged 5 to 9 are randomly selected and each is tested for skin allergies. Nine children are found to have skin allergies. Is there any evidence to suggest that children in this age group have a lower incidence rate of skin allergies? Justify your answer.