Ch 3 - 48E

Answer: Step 1 of 3 Given that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children. Let X be the number in the sample who have a food allergy. Then X ~ B(25, 0.05) a. We need to determine P(X 3) and P(X < 3) P(X 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) Using Excel function, “=BINOMDIST(x,n,p,false)” x P(x) 0 0.277389573 1 0.36498628 2 0.230517651 3 0.093015894 Sum 0.965909399 Therefore, P(X 3) = 0.9659. Now, P(X < 3) x P(x) 0 0.277389573 1 0.36498628 2 0.230517651 Sum 0.872894 Therefore, P(X < 3) = 0.8728