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 s 2) and P(X < 2). P(X S 2) = P(X < 2) = (b) Determine P(X 2 3). P(X 2 3) = (c) Determine P(1 sXs 2). P(1 sxS 2) = (d) What are E(X) and o,? (Round your answers to two decimal places.) E(X) = (e) In a sample of 70 children, what is the probability that none has food allergy? You may need to use the appropriate table in the Appendix of Tables to answer this question.

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