NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(25, .05).

a. Determine both P(X <= 3) and P(X < 3).
b. Determine P(X >= 4). c. Determine P(1 <= X <= 3).
d. What are E(X) and Sigma (x)?
e. In a sample of 50 children, what is the probablity that none have a food allergy?