Medical Tests: Leukemia Healthy adult bone marrow contains

Chapter , Problem 10

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Medical Tests: Leukemia Healthy adult bone marrow contains about 56.5% neutrophils (a particular type of white blood cell). However, if this level is significantly reduced, it may be an early indicator of leukemia (Reference: Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse). (a) In a laboratory biopsy, a field of n 50 bone marrow cells are observed under a microscope. A special dye is inserted, which only the neutrophils absorb. Then the number r of neutrophils in the field is counted. Although the field size n 50 is fixed, the number of neutrophils r is a random variable, so the proportion p r/n is also a random variable. Explain why p can be approximated by a normal random variable. What are mp and sp? (b) Suppose Jan had a bone marrow biopsy and p was observed to be 0.53. Assuming nothing is wrong (no leukemia), what is the probability of getting a biopsy result this low or lower? Compute P(p 0.53). (c) Suppose Meredith had a bone marrow biopsy and p was observed to be 0.41. Assuming nothing is wrong (no leukemia), what is the probability of getting a biopsy result this low or lower? Compute P(p 0.41). (d) Interpretation: Based on the probability estimates in parts (b) and (c), which do you think is the more serious case, Jan or Meredith? Explain.