The rarest white blood cell is the basophil, which constitutes only 1% of the total white blood cells. Students who are learning to perform white blood cell counts are inclined to mistake other cells for basophils until they have seen them often enough to recognize them. Thus a student's proficiency in performing differential white blood cell counts can be tested by checking whether too many cells have been recorded as basophils. This can be thought of as a Poisson process in which the interval is a count of 100 white blood cells.
a. State a null hypothesis indicating that the student can accurately identify the different kinds of white blood cells.
b. State an alternative hypothesis indicating that the student mistakes other cells for basophils.
c. The instructor decides that any student who records 4 or more basophils per 100 cells counted cannot yet distinguish these cells properly. How likely is it that a student will record cells correctly but have an unusual random sample of cells?
d. The frequency of basophils increases after surgery. Suppose the student is counting white blood cells from a blood smear taken under such conditions and l = 2.4 per 100 cells. How likely is it that fewer than 4 basophils are among the 100 cells counted? Should the instructor take precautions that the students are not using blood smears from postoperative patients?