Pediatrics, Otolaryngology Otitis media is a disease that occurs frequently in the first few years of life and is one of the most common reasons for physician visits after the routine checkup. A study was conducted to assess the frequency of otitis media in the general population in the first year of life. The table below gives the number of infants of 2,500 infants who were first seen at birth who remained disease-free by the end of the ith month of life, /-0, 1,..., 12. (Assume no infants have been lost to follow-up.) 7 0 1 2 3 4 5 6 7 8 9 10 11 12 Disease-free infants at the end of month i LAUSE SALT 2,500 2,400 2,400 2,325 2,205 1,975 1,900 1,725 1,525 1,325 1,275 1,250 1,225 (a) What is the probability that an infant will have one or more episodes of otitis media by the end of the sixth month of life? What is the probability that an infant will have one or more episodes of otitis media by the end of the first year of life? (b) What is the probability that an infant will have one or more episodes of otitis media by the end of the ninth month of life given that no episodes have been observed by the end of the third month of life? (Round your answer to four decimal places.) (c) Suppose an "otitis-prone family is defined as one in which at least three siblings of five develop otitis media in the first 6 months of life. What proportion of five-sibling families is otitis prone if we assume the disease occurs independently for different siblings in a family? (Round your answer four decimal places.) (d) What is the expected number of otitis-prone families of 100 five-sibling families? (Round your answer to two decimal places.)

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