Letxbe a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume thatxhas a distribution that is approximately normal, with mean=6100and estimated standard deviation=2750.A test result ofx<3500is 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,xis less than 3500? (Round your answer to four decimal places.) _________

(b) Suppose a doctor uses the averagexfor two tests taken about a week apart. What can we say about the probability distribution ofx?

• The probability distribution ofxis not normal.
• The probability distribution ofxis approximately normal with_x= 6100 and_x= 2750.
• The probability distribution ofxis approximately normal with_x= 6100 and_x= 1375.00.
• The probability distribution ofxis approximately normal with_x= 6100 and_x= 1944.54.

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

(c) Repeat part (b) forn= 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 asnincreased?

• The probabilities increased asnincreased.
• The probabilities decreased asnincreased.
• The probabilities stayed the same asnincreased.

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

• 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.
• 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.
• 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.
• 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.