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.) USE SALT (a) Determine both P(X ≤ 3) and P(X < 3). P(X ≤ 3) = 0.142 P(X < 3) = (b) Determine P(X ≥ 4). P(X ≥ 4) = (c) Determine P(1 ≤ x ≤ 3). P(1 ≤ X ≤ 3) = (d) What are E(X) and σx? (Round your answers to two decimal places.) E(X) = (e) In a sample of 50 children, what is the probability that none has a food allergy?

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