Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood.  Assume that x has a distribution that is approximately normal with mean of 7500 and estimated standard deviation of 1750.  A test result of x<3500 is an indication of leukopenia.  This indicates bone marrow depression that may be the result of a viral infection. What is the probability that on a single test x<3500? Suppose that a doctor uses the average for two tests taken a week apart.  What can we say about the probability distribution of ?  What is the probability that <3500? Repeat part b with n = 3 tests taken a week apart. Compare your answers for parts a, b, and c. How did the probabilities change as n increased?  If a person had <3500 based on three tests, what conclusion would you draw as a doctor or a nurs

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 8E
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Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood.  Assume that x has a distribution that is approximately normal with mean of 7500 and estimated standard deviation of 1750.  A test result of x<3500 is an indication of leukopenia.  This indicates bone marrow depression that may be the result of a viral infection.

  1. What is the probability that on a single test x<3500?
  2. Suppose that a doctor uses the average for two tests taken a week apart.  What can we say about the probability distribution of ?  What is the probability that <3500?
  3. Repeat part b with n = 3 tests taken a week apart.
  4. Compare your answers for parts a, b, and c. How did the probabilities change as n increased?  If a person had <3500 based on three tests, what conclusion would you draw as a doctor or a nurse?
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What is the Z value of calculating probability of x<3500, on a single test?

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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,