Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6350 and estimated standard deviation σ = 2600. 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.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

           a) The probability distribution of x is not normal.

           b) The probability distribution of x is approximately normal with μx = 6350 and σx = 1838.48.    

           c) The probability distribution of x is approximately normal with μx = 6350 and σx = 1300.00.

           d) The probability distribution of x is approximately normal with μx = 6350 and σx = 2600.

What is the probability of x < 3500? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

           a) The probabilities stayed the same as n increased.

           b) The probabilities increased as n increased.    

           c) The probabilities decreased as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

           a) It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

           b) It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.    

           c) It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

           d) It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.