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A differential is a type of white blood cell test where a certain number n of white blood cells are randomly selected from a patient.

A differential is a type of white blood cell test where a certain number n of white blood cells are randomly selected from a patient. White blood cells are classified into one of 5 categories, specifically, basophils (0.5%), eosinophils (1.5%), monocytes (4%), lymphocytes (34%), and neutrophils (60%). The percentages listed are the proportions of each type in healthy people. It is known, for instance, that an excess of lymphocytes is typical of a viral infection like hepatitis. Suppose a differential is performed on n = 100 white blood cells and and it is found that 48 of these are lymphocytes. Use this information to construct a 95% confidence interval for p the actual proportion of lymphocytes in this patient. What is the conclusion of your result?

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