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Ask Your Teacher NBC News reported on May 2, 2013, that 1 in 20 children in...

Ask Your Teacher 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 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.)

(a) Determine both P(X ≤ 2) and P(X < 2). P(X ≤ 2) = P(X < 2) =

(b) Determine P(X ≥ 3). P(X ≥ 3) =

(c) Determine P(1 ≤ X ≤ 2). P(1 ≤ X ≤ 2) =

(d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX =

(e) In a sample of 30 children, what is the probability that none has a food allergy?

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