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=7000and 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 approximately normal with_x= 7000 and_x= 1375.00.

The probability distribution ofxis not normal.

The probability distribution ofxis approximately normal with_x= 7000 and_x= 2750.

The probability distribution ofxis approximately normal with_x= 7000 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.