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According to a study, 45% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home.) Suppose that a survey is administered and 117 of 209 respondents indicated that they live at home. (a) Use the normal approximation to the binomial to approximate the probability that at least 117 respondents live at home. (b) Do the results from part (a) contradict the study